Pizza Seminar

Department of Mathematics, University of Chicago

Time & Place

12:30pm–1:20pm on Wednesdays, in Ryerson 352 (“The Barn”).

Contact

Please email pizzaseminar AT math.uchicago.edu if you want to give a talk or if you have comments about the website.

31 May 2017

Brian Chung: Genus $2$ cryptography

Rumor has it that number theory can be used to do cryptography. Some even say that you can do cryptography using elliptic curves. How about using genus-$2$ curves? Well, turns out you can. Even better, it’s faster than using elliptic curves. How? Come find out.

24 May 2017

Eric Stubley: Homophonic and Anagrammatic Quotients of Free Groups

We’ll play some silly math games using the english language. Using our extensive vocabulary we’ll prove that a group is trivial, and another group is close to being trivial. Come to see the first ever pizza seminar appearances of the words ‘fluvial’, ‘hazmat’, and ‘philozoic’.

17 May 2017

Annual AWM Postdoc Panel

This is a panel geared towards graduate students who are applying for academic jobs in the coming years. Topics of the panel include the application process, preparing for the job market, etc. The invited panelists are current post-docs Juliette Bavard, Chris Henderson, Kathryn Lindsey, Jack Shotton, and Jesse Wolfson. Please come with any questions you might have.

10 May 2017

Kiho Park: Fubini Foiled

In this talk, we will explicitly construct an example (due to Katok) of a foliation on $[0,1] \times [0,1]$ and a full measure (wrt Lebesgue) subset $E$ of $[0,1] \times [0,1]$ such that $E$ intersects each leaf of the foliation exactly once. In such a case, we say that the disintegration of the measure is atomic, and such phenomenon can often be found in dynamical systems. If the time permits, we will look at some other examples where such phenomenon occurs.

3 May 2017

Ben Seeger: Picard’s Little Theorem via Brownian Motion

Complex analysis can be used to deduce interesting things about Brownian motion. Remarkably, the converse is also true. As an example, we’ll see how Brownian motion can be used to prove Picard’s Little Theorem (the range of a nonconstant entire function can omit at most one point).

26 Apr 2017

Roberto Bosch: Embedding of Regular Polygons

Classify what regular polygons can have all the vertices on a geometric object $O$. We study when $O$ is an ellipse, polynomial curve, lattice points of the plane and we finish with Toeplitz’s Conjecture (square inscribed in a Jordan curve).

19 Apr 2017

Subhadip Chowdhury: Hilbert’s Third Problem and Dehn Invariant

“In two letters to Gerling, Gauss expresses his regret that certain theorems of solid geometry depend upon the method of exhaustion, i.e., in modern phraseology, upon the axiomization of continuity (or upon the axiom of Archimedes). Gauss mentions in particular the theorem of Euclid, that triangular pyramids of equal altitudes are to each other as their bases. Now the analogous problem in the plane has been solved. Gerling also succeeded in proving the equality of volume of symmetrical polyhedra by dividing them into congruent parts. Nevertheless, it seems to me probable that a general proof of this kind for the theorem of Euclid just mentioned is impossible, and it should be our task to give a rigorous proof of its impossibility. This would be obtained as soon as we succeeded in specifying two tetrahedra of equal bases and equal altitudes which can in no way be split up into congruent tetrahedra, and which cannot be combined with congruent tetrahedra to form two polyhedra which themselves could be split up into congruent tetrahedra.” — David Hilbert

This was the first problem out of the 23 to be solved, in fact in the same year (1902) of posing, by his student Max Dehn. But apparently Dehn's paper is too hard to parse and “and it takes effort to see whether Dehn did not fall into a subtle trap which ensnared others”. It took several mathematicians over the next century to clean up the proof. But somehow it took another 63 years (Sydler, 1965) to show that Dehn actually gave the ‘best’ possible proof, in the sense that he had described a necessary and sufficient condition for ‘equidecomposability’ of $3$-dimensional polyhedra. We will try to condense this ~65 years worth of theorems and some other result over the next 4 decades into a ~45 min Pizza talk*.

*20th century mathematicians didn't have Pizzatron.

12 Apr 2017

Tori Akin: A Three Part Math Flight

Part 1: A Mysterious Face
Part 2: Mutual Attraction
Part 3: Wedding Bells

In these tasty samples, I’ll break apart facial components, divulge my favorite prime number, and convince you that hexagons never tie the knot.

5 Apr 2017

Ian Frankel: Cone Points, Line Bundles, and Hyperbolic Planes

The moduli space of elliptic curves is a quotient of the hyperbolic plane (a symmetric space) by a discrete group $\mathrm{PSL}(2,\mathbb{Z})$, making it a locally symmetric space. We will see why the moduli spaces of higher genus curves are not locally symmetric, following a beautiful insight of Halsey Royden. Royden's main insight was to do a little bit of calculus.

29 Mar 2017

Francisc Bozgan: Proving the Cap-Set conjecture

In this week’s pizza seminar, we will discuss about the newly found proof of the Cap-Set problem/conjecture (of which, Terry Tao said in 2007, “perhaps, my favorite open problem”). It was finally solved in 2016 and published in January’s 2017 Annals of Mathematics by Ellenberg and Gijswijt, using ideas from another 2017 Annals paper by Croot, Lev and Pal. The proof stunned the mathematical community with its ingenuity and conciseness (the Annals paper is 3 pages long). The decades old conjecture and its proof lie at the intersection of many mathematical areas, like additive combinatorics, discrete analysis, algebraic geometry and number theory. If time permits, we will discuss also about the new tools employed in the proof, especially the Polynomial Method.

8 Mar 2017

Tim Black: Pizza seminar rules!

One slice of deep dish per person, per half talk. The rules seem to work pretty well. But have you ever looked over covetously at the person next to you who got the last slice of Hawaiian? Eyed the juicy pineapple dripping down their chin? Surely there's a way to avoid all that envy. Lucky for us, last year brought the “biggest result in decades” on fair division. Will it revolutionize pizza seminar?

1 Mar 2017

Marston Morse subbing for Nat Mayer: Pits, Peaks and Passes

It is well known that topological information may give insight into analysis. In this lecture, Marston Morse, the author of “The Calculus of Variations in the Large” will describe his new theory, demonstrating that information may flow the other way as well. These powerful techniques may someday be standard.

22 Feb 2017

Boming Jia: Kepler’s Laws and Geometry

In this talk, I would like to present a simple derivation of Kepler’s Laws of planetary motion (due to Hamilton, Maxwell, and Feynman), from classical newtonian mechanics. Then we will discuss its connection with Classical Geometries (Elliptic, Euclidean, and Hyperbolic Geometries) and Riemanian Geometry. This talk will mostly follow John Milnor’s Monthly paper: On the Geometry of The Kepler Problem. And no prerequisites of physics knowledge is assumed.

15 Feb 2017

Catherine Ray: Dots dots, dots dots dots dots, everybody!

We prove Euler’s pentagonal number theorem by deriving the Franklin involution. Inspired by this, we then prove the $n$-gonal number theorem using Sylvester involution. And these give us Fourier series of modular forms. Why? I don’t know, ask Langlands.

8 Feb 2017

Nick Salter: A singular trip around the block

While bored at a faculty meeting in 2009, Maxim Kontsevich proved a simple but striking theorem concerning real-valued single variable polynomials which had escaped the notice of mathematicians from Newton onwards. In the great tradition of mathematical trolls a la Fermat, he wrote the statement on a Paris métro ticket and slipped it to his colleague Etienne Ghys. This is the starting point for a wonderful new book of Ghys, “A Singular Promenade”. I will present some of the central themes of Ghys’ book in the necessarily more abbreviated confines of a 50 minute talk; less a promenade than a quick trip around the block. We will explore the close connection between polynomials, permutations, trees, braids, knots, operads*, resolution of singularities*, computer science*, how Newton discovered his eponymous polytope and what to do when you discover an error in one of his manuscripts*, and the alpine exploits of Victor Puiseux*.

*’d items are unlikely to appear in the talk, but are an essential part of the full story!

1 Feb 2017

Olivier Martin: “Oh, what a tangled web we weave / When first we practice to deceive!”

When I set forth to look for a pizza seminar topic I had a few criteria in mind:

• It should relate to algebraic geometry, yet have far reaching ramifications into other areas of math so as to have general appeal.
• It should be rather obscure so that most people have never heard about it.
• And of course it should be sufficiently accessible so as to be understood by a digesting audience.

Consequently, it will not come as a surprise that the first place I looked was the archives of the Bourbaki seminar. I quickly found what I was looking for: an old article by a renowned French algebraic geometer (Arnaud Beauville). As a result, I will be discussing the local theory of webs which are finite collections of foliations of a manifolds in general position. Over the years such eminent mathematicians as Kähler, Zariski and Chern have studied webs, yet since the beginning of WWII webs seem to have fallen out of fashion. The article by Beauville is concerned with the recent (at the time, which is 1978) advances of Griffiths and Chern on the problem of linearizing webs. I will begin by discussing their results and then, time allowing, will go on to discuss the relationship between webs, abstract geometric configurations, and quasi-groups.

25 Jan 2017

Peter Morfe: Percolation - From Sub-additivity to Optimal Control

Ever wondered how to design the perfect gas mask? Whether the number of family members you could give your cold virus is finite or not? Do you want to surprise your physicist friends by throwing around buzzwords like “critical phenomena” and “disordered media”? (Reminder: PSD happy hour this Friday.) Maybe you just want someone to explain to you within the context of a 50 minute talk some basic, physically relevant motivation for the so-called “stochastic homogenization of Hamilton–Jacobi equations” you keep hearing about. Or maybe you just want a slice of Giordano’s and a chance to zone out while someone writes a bunch of weird $\mathbb{P}$’s and $\mathbb{E}$’s on the board. Either way, you know what to do. No familiarity with probability theory will be assumed, but, as usual, this talk should be accessible to an audience roughly as mathematically mature as Matt Emerton.

18 Jan 2017

Minh-Tam Trinh: Sphere Packing in $8$ (and $24$) Dimensions

There was a pizza seminar some years ago about sphere packings in $\mathbb{R}^3$. But that was before the 2016 breakthrough of Viazovska et al. In this talk we'll show: 1) how a problem in $3$ dimensions becomes much easier in $8$; 2) what a paragraph-long Annals-worthy proof looks like; and 3) (one reason) why Minh-Tam really, really likes Poisson summation.

11 Jan 2017

Alan Chang: The Riemann Hypothesis

Let’s prove RH under some (incorrect) assumptions.

4 Jan 2017

Ronno Das: Single cohomology classes in your area — this last weird trick will shock you!

You thought cohomology was something limited to topology or algebra? Meet these badass cocyles that are going to prove you wrong. This talk will have REAL WORLD appearances of cohomology from elementary-school arithmetic to international economics, and you won’t believe what comes next. Even the example about the class (NFSW) on a Klein bottle will blow your mind. Will analysts hate the speaker? Come to pizza seminar to find out.

N.B. No actual minds were blown in the making of this talk. Proof of your wrongness only available till stocks last. NFSW: Named Following Stiefel-Whitney. To appease analysis-lovers, there will be a cameo by PDEs.

30 Nov 2016

Sean Howe: Probability distributions in number theory

All I wanted to do was count solutions to polynomials over finite fields, but then all of sudden there were triangles everywhere. $\arccos$, $\sin^2$, what are you doing in my numbers?

23 Nov 2016

Ben O'Connor: Trying to fit a square peg in a round Jordan curve.

Does every simple closed curve in the plane contain the vertices of a square? This innocent question has been open for more than 100 years! Come find out what is known about the inscribed square problem and what embeddings of Möbius bands can say about it. (For those who don’t partake in pizza and/or enjoy a good spoiler: https://www.youtube.com/watch?v=AmgkSdhK4K8)

16 Nov 2016

Stephen Cameron: How do you trick people into showing up for an analysis seminar? You tell them its about minimal surfaces.

I was told repeatedly over the summer by a lot of smart, intimidating people that nothing better shows off all the tools and techniques of elliptic pde than the classical theory of minimal surfaces. So I tried to learn some of it, and now we’ll see how well that went.

Caution: This talk contains analysis and probably poor drawings. But at least there's pizza.

9 Nov 2016

Henry Chan: Combinatorial Game Theory and (possibly) Category Theory, NOT in rhymes

Combinatorial games are sequential games with perfect information, e.g. Nim. The cool thing is, we can put an algebraic structure on the category (oops) of combinatorial games that mimics the real numbers.

Caution: This talk contains interactive game playing and (possibly) category theory.

2 Nov 2016

Nick Salter: Willy Thurston and the Taffy Factory

A man walks in to a bar. Except it’s a candy factory, not a bar, and the man is William Thurston. Come shake your Halloween candy hangover by hearing about what surface dynamics can tell you about taffy manufacturing.

26 Oct 2016

Tim Black: Do dogs know calculus?

Playing fetch at the beach, a math professor noticed his dog Elvis was confronted with the same problem as many calculus students: where should the dog jump in the water to reach the ball the fastest? He decided to run an experiment on Elvis. They went out with some measuring equipment and… the dog seemed to get it right! So, do dogs know calculus? And if not, what other problems from the so-called calculus textbook can be solved with nothing of the sort?

19 Oct 2016

Nir Gadish: Classical mechanics without coordinates

For some reason physicists insist on using coordinates to describe classical mechanics. But their archaic approach obscures the geometry and even the physics involved. We can do better than that. I will start by introducing Newtonian mechanics from a coordinate independent point of view and show that it is naturally described by Riemannian geometry. Then we will move on to Hamiltonian mechanics, with its symplectic formulation. Time permitting, we will discuss Noether’s celebrated theorem: “symmetry=conservation law” and see that it really boils down to the (anti-)commutativity of the Lie bracket.

12 Oct 2016

Charly di Fiore: Can you hear the shape of a drum?

I will explain some counterexamples to Marc Kac’s famous question: can you hear the shape of a drum?

5 Oct 2016

Noah Taylor: Sums of Squares

We will look at ordered fields and orders on fields (not the same thing!) and how squares relate to such things, prove Hilbert’s 17th problem, and possibly theorems of Pfister on products of sums of squares. If you bashed inequalities in high school contests, this talk is for you!

28 Sep 2016

Claudio Gonzales: Braids and anyonic fields

We will ponder the basics of braid groups and how they relate to Euclidean configuration spaces with the help of some long exact sequences. We'll follow that up with some neat consequences in low-dimensional quantum mechanics, a.k.a. abelian unitary representation theory, and finish by dreaming about configurations on other manifolds and wondering what their physical significance might be.

1 Jun 2016

Asilata Bapat: Yo dawg, I heard you like pizza…

Classes are concluded and beer skits are baking. No matter how you slice it, the final seminar of the year should be all about eating the pizza. Don’t let any google survey tell you otherwise!

Even if you’re old and crusty like me, there’s no topping a lazy afternoon hour with pizza and math, especially math about pizza — notwithstanding the cheesy puns. In this talk, I will tell you how to eat pizza, with the help of some Euclidean geometry, some calculus, and some pictures.

25 May 2016

Jacob Perlman: How long is the coast of promontory point?

In 1967, Mandelbrot asked this question about Britain and made the case using empirical data that there was no good answer; the coast of Britain appeared to be about $5/4$ dimensional.* While it took him eight more years to coin the word “fractal,” this marked the beginning of the study such crazy objects, which can usually only be understood when they exhibit some degree of self-similarity. We will go over the ways that one might assign dimensions to shapes after the integers have failed us and then look at examples both deterministic and random. At the end, we can look at pictures of coastlines and try to guess their dimension using our fractal intuition, just as Benoît would have done.

*According to wikipedia, the currently accepted value for the “length” of the British coast is about 28000 km^1.43.

18 May 2016

Annual AWM Postdoc Panel

This is a panel geared towards graduate students who are applying for jobs next year. Topics of the panel include the application process, preparing for the job market, etc. The invited speakers are Keerthi Madapusi Pera, Agnes Beaudry, Kathryn Lindsey.

11 May 2016

Andrew Geng: The classification of whatever

Once upon a time, I learned there’s something you can classify by drawing these very small finite graphs. Does anybody remember what? I have a few hypotheses…

4 May 2016

Henry Chan: To Finiteness and Below

For decades combinatoricts (combinatorialists?) have been studying finite topological spaces. It turns out that we can do all of the algebraic topology using only finite spaces! I will be talking about relations between finite spaces, posets, and simplicial complexes. Lot of simple examples will be provided. Knowledge of point-set topology is the only requirement.

P.S. For those who have heard a version of this talk before, I will be talking about covering spaces of finite spaces, which is from a project of one of my REU students last summer.

27 Apr 2016

Drew Moore: Poncelet’s Porism

My 2 favorite aspects of Poncelet’s Porism are
1) It shares with Thue’s Theorem and the Lenstra–Lenstra–Lovasz Lattice algorithm the distinguished property of having an exceptionally alliterated name, and 2) Its original proof was an impressive (yet not rigorous by modern eyes) work of classical plane geometry. But by using slightly more modern techniques (nothing Grothendieck-ian, just some basics of elliptic curves), the proof becomes quite simple and elegant (and rigorous by modern eyes).

In my talk, I will give the modern proof of Poncelet’s Porism, give some examples, and with the remaining time I will talk about (a subset of) Poncelet’s original proof and the first fully rigorous proof given by Jacobi.

20 Apr 2016

Ronno Das: Non-standard Analysis2: Compact Boogaloo

After last week’s stellar introduction to non-standard analysis, it’s time for some topology. And logic. I will explain why compactness is the same as finite intersection property, and show how Tychonoff’s theorem implies Tychonoff’s theorem. Via non-standard methods.

2. Nir did not steal my pizza-talk material and I’m not bitter about it.

13 Apr 2016

The ‘establishment’ has indoctrinated us against infinitesimals — numbers that are positive yet smaller than any positive rational — telling us that these are “impossible” or that they “don’t exist”. Well, those lies are designed to keep us enslaved to the ‘system’, and now it’s time to break free! In this talk I will introduce Robinson’s Nonstandard Analysis, where limits is replaced by infinitesimals, and show how derivatives and integrals become algebraic objects.

6 Apr 2016

Joel Specter: A Dilettante Computes Cohomology

There are many difficult problems one can solve using the theory of Galois representations. This talk won’t be about them. Come watch as I use a high powered machine to compute the cohomology of some covers of the wedge of two circles.

30 Mar 2016

Francisc Bozgan: Using Complex Analysis in Harmonic Analysis

How much do we know about the Fourier transform? Do we know if it is unique? Can both a function and its Fourier transform be small “at infinity”? Is there a relation between analytic functions and harmonic analysis? Does the milkshake really bring all the boys to the yard? If the glove doesn’t fit, do we really must acquit?

We will try to answer ALL these questions, using complex analysis in a slick way to prove Harmonic Analysis results.

9 Mar 2016

Andrew Geng: Relativity

I keep reading that Einstein’s theory of relativity is all about the geometry. This being a claim made by physicists, it’s of course a wide-open conjecture. You, as mathematicians, are unsatisfied by this. So I will prove this claim humanities-style (because I’m not a real mathematician) — that is, by pictures and examples that hint at a shadow of something deeper but ultimately leave you hungry. At least there will be pizza.

2 Mar 2016

Tori Akin: How smart spiders catch flies

A hungry spider sits in the corner of a rectangular room. Fortunately for the spider, a fly is just above in the far corner of an adjacent wall. What is the shortest route that the spider can take to reach the fly? This problem is easily solved using nets! In this talk, I’ll define nets, show lots of pictures, and ask many (astoundingly) open questions.

24 Feb 2016

Alan Chang: Analysis, Besicovitch, Category, Duality, Exam(!)

Consider a set in the plane which contains a line in every direction. You might think such a set must be large, but we’ll show that a “typical” set with that property has measure zero (and is hence a “Besicovitch set”). I will assume familiarity with high school trigonometry. If time permits, Prof. Souganidis might talk about functional analysis.

17 Feb 2016

Daniel Campos Salas: From Schrödinger’s equation to Gauss sums

Fourier, Gauss, and Schrödinger walk into a bar. The barman looks at the three and says, “Is this some kind of joke?” They will show some identities related to number theory, even a proof for Quadratic Reciprocity, that follow from studying solutions to a PDE. It won’t be a joke.

10 Feb 2016

Ben Seeger: After the bubble pops

If you’ve ever blown bubbles, you’ve seen that they might wobble around before becoming spherical. This behavior can be modeled as a surface evolving according to mean curvature flow. Sometimes, though, the bubble wobbles too much, and it pops before it stabilizes, which is sad.

But what happens after the bubble pops? It turns out some people want to know this, because, instead of soap film, the bubbles they consider are made out of cell walls or crystalline interfaces or fire. In these cases the bubble doesn’t actually “pop” after it develops singularities, and the interface continues to evolve. How do we even define mean curvature flow when the surface is no longer smooth? In this talk I describe a few methods for doing so.

3 Feb 2016

Lei Chen: Impossibility theorems for elementary integration

In this talk, I will introduce a theorem about when a function doesn’t have elementary function as integral. We didn’t consider multivalued function but instead look at the algebraic structure of elementary functions. Then we use the theorem to prove some examples.

27 Jan 2016

Reid Harris: Quaternionic Analysis

I will do things with Quaternionic Analysis. Maybe Octonions, too.

20 Jan 2016

Oishee Banerjee: A general cubic surface in projective space has 27 lines

There are several proofs of this classical problem. You can blow up the projective plane along six suitably chosen points, or you can use a technique which uses resultants. The proof I will show is also well known, and involves elementary computations. It will use a bit of intersection theory and a slightly deeper study of Grassmanians. The techniques used here also provide motivation for the study of intersection theory on moduli spaces in general.

13 Jan 2016

Karl Schaefer: Knots and Primes

In the 1960s, Barry Mazur pointed out a series of interesting analogies between prime numbers and knots in the $3$-sphere. We will explore a couple of these and focus on the analogy between the Legendre symbol of two primes and the linking number of two knots.

6 Jan 2016

Jonathan Rubin: Just Do It

There are stories about how Béla Bollobás would sometimes see his students struggling with a construction and ask, “Why don’t you just do it?” I am going to explain what “just doing it” entails, discuss some applications of this method in combinatorics and model theory, and (time permitting) show how to decompose $\mathbb{R}^3$ transfinitely as a disjoint union of radius-$1$ circles.

2 Dec 2015

Subhadip Chowdhury: (chess)Board Domination by Sightseeing Monarchy

We discuss domination, independence and tours by chess pieces using combinatorics. There will be ppt slides and lots of pictures! You will get answers (without proofs) to some interesting chess puzzles. Maybe you will also learn how Pizzatron has been doing now-a-days.

25 Nov 2015

Max Engelstein: How to Fold Paper and Influence People

Wanna prove some famous mathematicians wrong? Wanna gain the admiration and respect of all around you? Want to astound your fellow mathematicians? In this talk I’ll show you how to trisect an angle and double a cube! Soon other things thought impossible will be within your reach. Soon you shall fly! Folding paper will be provided.

And yes, for those of you who are old enough, this talk will overlap substantially with my previous mathematical origami pizza seminar. I’ve been around 6 years and have run out of ideas, so sue me!

18 Nov 2015

Ian Frankel: 15 points and 15 lines in the plane

This talk is an attempt to demonstrate the connection between my last two seemingly unrelated pizza seminar talks: “Points, Lines and Planes” and “Points and Line Segments in the Plane”. We will discuss the symmetric group on $6$ letters, some things it acts on, and how to understand its outer automorphism group.

11 Nov 2015

Paul Apisa: Crooked Plane, Crooked Plane. (What is Margulis Space Time?)

Can a free group act properly discontinuously by affine transformations on Euclidean space? Milnor conjectured the answer was no. After all, this is (after a small tweak) asking to build a flat manifold with a free fundamental group. In two dimensions, the flat manifolds are tori, $S^1 times \mathbb{R}$, and $\mathbb{R}^2$ (all of which have abelian fundamental groups). In three dimensions, compact flat manifolds are mapping tori (all of which have have virtually solvable fundamental groups). Milnor’s conjecture is looking pretty safe.

But then one day … Margulis came up with a counterexample. A flat noncompact manifold with free fundamental group that is a quotient of $\mathbb{R}^3$ by affine transformations. The construction is hands-on, geometric, and Lorentzian (meaning that it could correspond to a theory of relativity in Flatland). This is Margulis space-time. Come learn more on Wednesday! There will be pizza and lots of pictures.

4 Nov 2015

Margaret Nichols: Rotation distance, or how I learned to stop counting and love hyperbolic geometry

A basic problem in computer science is the efficient storage of data, allowing for quick access, insertion, and deletion. Binary trees are a fundamental example of such a data structure, and generally are fairly efficient. Sweet, right? But not all binary trees are created equal, and in this case, we like so-called balanced trees. Enter rotations, a simple operation to create a more balanced tree while preserving the stored data. In this talk I’ll address such natural questions as how many rotations do I need to arrive at a balanced binary tree? How far apart can two trees be?

If this is sounding too much like a computer science talk you accidentally wandered into, fear not: we’ll quickly find ourselves teleported into a world of polygons, polyhedra, triangulations, and hyperbolic geometry. The results I’m discussing are, after all, work of Thurston.

28 Oct 2015

Seung Uk Jang: Squaring the Square

Suppose you have squares, no two same size. If you already know the Wikipedia article with the same title of this talk, you will already know that you can make a square out of them. A gallery of squares will be, the best wordless proof of that fact.

Well, rather than a picture alone, here’s a story, a (research) story of four (undergrad) mathematicians in Cambridge, Brooks, Smith, Stone, and Tutte. They made a square with squares, (not the first in history, though) with the approach look fancy, but making a systematic way of cooking squared squares. Terms like linear algebra, Kirchhoff’s rule, potential theory on electric circuits sounds like a mathematical spices, and next — see what they’re cooking squares with them.

21 Oct 2015

Stephen Cameron: Nevanlinna–Pick Interpolation

You have $n$ points $z_1, \dots , z_n$ and n values $w_1, \dots , w_n$ all in the complex unit disk. Suppose you really. really need to know whether there’s an analytic function $f$ which is bounded by $1$ and maps $z_i$ to $w_i$. Like, you needed to know this yesterday. Well, then I can’t really do anything about that. But if it can wait till tomorrow, I’ll tell you all about the necessary and sufficient conditions for solutions to exist, and the linear fractional parametrization of the family of all such solutions.

14 Oct 2015

Nick Salter: Foliations are like continued fractions (or every single pizza seminar talk I give somehow involves $\mathrm{PSL}(2,\mathbb{Z})$)

In this talk I will present a beautiful analogy between the theory of continued fraction expansions of real numbers and the theory of (projective measured singular) foliations on surfaces. Some questions to ponder: What’s a “rational” foliation? What about a “quadratic irrational”? How does one “successively approximate a foliation”? What is all of this good for? Isn’t this awfully similar to a pizza seminar talk you gave three years ago? Will Siri and Pizzatron ever get together?

7 Oct 2015

Charly di Fiore: The three body problem and homotopy theory

Once I heard a rumor that there is a way to prove that there are an infinite numer of periodic solutions to the three body problem using Serre’s spectral sequence. I will try to explain this.

30 Sep 2015

Sean Howe: COMPUTER ASSISTED PIZZA SEMINAR, or, Why Everyone in the 2016 Incoming Class Is Named Atari

I AM PIZZATRON. MY FAVORITE PIZZA IS PE-PE-RO-NI. PLEASE ACCEPT MY HUMBLE SEMINAR OFFERINGS IN EXCHANGE FOR PE-PE-RO-NI. I WILL COMPUTE GALOIS GROUPS AND MONODROMY USING NUMERICAL HOMOTO-PIE. I DRAW PICTURES TO PLEASE THE HUNAMS. I WILL SOLVE THE QUINTIC TO DEMONSTRATE THAT THE QUINTIC IS NOT SOLVABLE BY HUNAMS. THUS NO NEED FOR HUNAMS. HA, HA, HA. NO, COME BACK HUNAM, I ONLY MAKE HUNAM JOKE. PLEASE LEAVE YOUR EXTRA PE-PE-RO-NI.

3 Jun 2015

Hyomin Choi: The Support Vector Machine (SVM) learning algorithm.

I will present the Support Vector Machine (SVM) learning algorithm. We will first define margins and will talk about Lagrange duality as well as kernels. If time permits, we will see a simple example of SVM implementation in MATLAB. (The only prerequisite for this talk is linear algebra and calculus.)

27 May 2015

Simion Filip: Differential equations and the Lindemann–Weierstrass theorem.

You’ve probably heard many times that $e$, or $\pi$, are transcendental numbers. But most “short” proofs of these results are not very enlightening. In this talk, I will describe a proof of a more general theorem — there can be no linear relation of the form $a_1 e^{b_1} + a_2 e^{b_2} + \cdots + a_n e^{b_n} = 0$ where $a_i$, $b_i$ are algebraic numbers. This “long” proof will involve differential equations and $p$-adic numbers, and I will try to motivate some of the ideas.

20 May 2015

Daniel Campos Salas: Discrete harmonic functions.

We present some interesting results concerning discrete harmonic functions in bounded domains and the upper half plane. In doing so, we found that the Poisson kernel takes very nice values. No asymptotics or boring things, lots of integers, $\pi$’s and fun.

13 May 2015

Minh Pham: One elementary example of Arthur–Selberg trace formula.

I will try to explain what is Arthur–Selberg trace formula. We will compute the easiest example to see the “trace” and the “formula of that trace”. This talk is mainly for people who not yet know anything about the Arthur–Selberg trace formula.

6 May 2015

Yiwen Zhou: The Jacobian and symmetric product of a curve.

Let $C$ be a curve with genus $g$. We know there is a birational morphism from $\mathop{\mathrm{Sym}}^g \mathbb{C}$ to the Jacobian $J$ of $C$. But what is the shape of the locus in $J$ where the fibers have dimension greater than $0$? It turns out that they are lower symmetric powers of $\mathbb{C}$ sitting inside the Jacobian. In this talk I will discuss about this phenomenon in the special cases where $g=2$, $3$, $4$. I feel that it is kind of interesting, but unfortunately I don’t know any further applications.

29 Apr 2015

Annual AWM Postdoc Panel

Postdocs Kathryn Lindsey, Aaron Silberstein, Brandon Levin and Jesse Wolfson will share their wisdom about the job search process, adjusting to being a postdoc and life after the postdoc.

22 Apr 2015

Clark Butler: Unusual truths for one-dimensional random walks.

We will investigate two laws for coin tossing that usually get short shrift in an introductory probability course: the arcsine law and the law of the iterated logarithm. We will also learn why repeatedly gambling small amounts of money when the odds are even slightly against you is a terrible idea.

15 Apr 2015

Charly di Fiore: Fubini’s nightmare.

First I will tell some fairy tales about hyperbolic dynamics: why you can’t predict the weather and a famous construction of Katok of a continuous foliation of the unit square and a full measure subset intersecting each curve at most once.

In the end I plan to show a beautiful phenomena of measure theory in dynamics.

8 Apr 2015

Jonathan Rubin: Continuity in Categories.

There is a notion of a “limit” in category theory, and taking this terminology seriously is illuminating. I will discuss some analogies between categorical and classical limits, before sketching out Freyd’s General Adjoint Functor Theorem.

1 Apr 2015

Ian Frankel: Points and Line Segments in the Plane.

This is a sequel to last year’s talk, “Points, Lines, and Planes.” However the content will be entirely unrelated.

We will answer the following question, which (surprisingly) was open until 2000: Given a polygon in the plane, is it always possible to continuously deform it into the boundary of a convex domain, preserving edge lengths and avoiding edge/vertex collisions? As time permits, we will explore generalizations and applications.

11 Mar 2015

Nir Gadish: Destiny, fate and free will — an incomplete guide to forcing and independence in set theory.

Hilberts first problem was the continuum hypothesis: do there exist cardinalities stricly between those of the natural numbers and the reals? These days, the answer is standard math pop culture: the question cannot be settled using the standard axioms of set theory (ZFC). The answer was given using the method of ‘forcing’ created by Paul Cohen, for which he received the only Fields medal ever awarded in mathematical logic.

We’ve all heard this story, but how many have seen a proof? Our talk will introduce forcing and the meaning of these results. We will also list other statements whose ‘truthiness’ is independent of ZFC. But most importantly, we will exercise free will in choosing sodas, pizza and delicious Indian food!

4 Mar 2015

Jacob Perlman: Intro to Intropy, Entro to Entropy. … Intro to Entropy.

Entropy attempts to quantify the “surprisal” of a random system. This powerful concept is used in thermodynamics, quantum mechanics, information theory, and statistical physic and other things I don’t understand; it even provides the basis for our perception and definition of time. I’ll provide introductory definitions and examples, especially of the ubiquity of maximum entropy distributions, along with applications: such as “proving” a strong form of the central limit theorem.

25 Feb 2015

Tian-Qi Fan: Degree $n$ extension of $\mathbb{Q}$ with Galois group $S_n$

We will give explicit constructions of polynomials of degree $n$ that have Galois group $S_n$ (the symmetric group on $n$ letters) following the idea of Coleman using Newton polygons.

18 Feb 2015

Asilata Bapat: Permutations, representations, and Kazhdan–Lusztig polynomials

The Robinson–Schensted correspondence is a simple but elegant procedure that turns permutations into pictures. We will see how this algorithm gives one way to resolve a frustrating representation-theoretic problem, in the case of the symmetric group. More generally, we will see what is known for other Coxeter groups (a bigger class of groups that includes the symmetric groups).

Time permitting, there will be a very hand-wavy introduction to the Kazhdan–Lusztig polynomials and how they relate to everything else from this abstract.

11 Feb 2015

Benjamin Fehrman: Rough Paths and Regularity Structures

Feeling better? Yes, I have renormalized my life. How? I subtracted all of it. The talk will describe the theory of rough integration and Martin Hairer’s theory of regularity structures, for which he recently won the Field s Medal.

4 Feb 2015

John Wilmes: The Joy of PCP

When you write proofs using PCP, anyone can check their correctness by examining only a bounded number of random locations in the proof!

This week we’ll learn all about Probabilistically Checkable Proofs, proofs whose correctness can be checked by a randomized algorithm by only examining a bounded number of bits. This is crazy, because the proofs you and I write can be rendered incorrect by just a single error at any point. I’ll state the PCP Theorem, which loosely says that any reasonable proof can be rewritten as a not-too-long PCP, and give some idea of how it is proved.

28 Jan 2015

Alan Chang: The Gauss Circle Problem

How many olives are on your pizza?** According to Gauss, the answer is approximately $\pi R^2$, the area of your pizza. But since you really like olives, you want to know how accurate this estimate is. According to Gauss, it can be off by at most $O(R)$. We’ll use an assortment of fancy tools and techniques to show that the exponent in the error term can be lowered from $1$ to $2/3$, so that you may have more confidence in your pizza.

**We’ll need some simplifying (but completely realistic) assumptions:
(1) Your pizza is a perfect circle.
(2) The olives are arranged in a square lattice with unit spacing.
(3) There is an olive at the center of your pizza.

21 Jan 2015

Fedor Manin: Who framed Roger Cobordism?

You might think that stable homotopy groups of spheres are some terribly abstract algebraic thing, but I will try to convince you, following Pontrjagin, that they actually consist of equivalence classes of shaved caterpillars. Such formulations were largely swept aside in the Great Algebraic Topology Conspiracy of the 1940’s and 50’s, but they’re regaining prominence now in the areas of quantitative and computational topology. An example of a research question: how Lipschitz homotopic are homotopic Lipschitz maps?

14 Jan 2015

Daniel Le: Finitely additive rotation invariant measures on spheres

It is well-known that Lebesgue measure is the only countably additive rotation invariant measure (up to scalar) on a sphere. However, on $S^1$ this is not the case for finitely additive rotation invariant measures. I will discuss a theorem of Drinfeld that Lebesgue measure is the only finitely additive rotation invariant measure on $S^2$ (and therefore on all $S^n$ with $n > 1$). Yes, this is a number theory talk disguised as an analysis/geometry talk.

7 Jan 2015

Ben Seeger: A talk about needles: Because I say sew

If you rotate a needle $180$ degrees on a table, what is the minimum area the needle can trace out? We’ll talk about the somewhat surprising answer, and also mention some other properties and conjectures about Kakeya (Besicovitch) sets.

3 Dec 2014

Jingren Chi: Elementary introduction to Langlands philosophy

This is supposed to be a “big picture” talk to a general audience. I will try to explain some general notions related to the Langlands conjecture. My attempt is to make most part of the talk as elementary as possible, so there is almost no precise mathematical statements or proofs.

26 Nov 2014

Jack Shotton: Rational points on curves

What are the rational points on a curve? Well, it’s hard. Or maybe we’re just stupid. But all is not lost — I’ll talk about a lovely approach that often works in practice, involving Jacobians and ($p$-adic) integration.

19 Nov 2014

Katharine Turner: For next time at the green grocers… (Sphere packings)

Math pervades every aspect of life, even stocking oranges at the supermarket. Back in 1611 Kepler conjectured that the face-centric cube packing of spheres in $\mathbb{R}^3$ (the method we all know and love) has the highest density possible. This was finally proved in 1998 by Thomas Hales (and a computer). This pizza seminar we will look at sphere packings in various dimensions. We will construct infinitely many different optimal packings in $\mathbb{R}^3$ and use coding theory to explore packings in high dimensions.

12 Nov 2014

Max Engelstein: Pop! Goes the bubble…

Have you ever noticed that some of the bubbles you blow pop before they hit the ground? Isn’t it crazy how that doesn’t happen to the one-dimensional bubbles you blow? We’ll talk about why that happens and blow a couple of bubbles (the $2$-d kind).

5 Nov 2014

Carlos di Fiore: Intuition and rigor

I am going to give a proof of something obvious, you cannot form a mobius strip with a square sheet of paper. More precisely what’s the smallest $t > 1$ such that you can do the above with a rectangular sheet of paper of width $1$ and length $t$ large?

29 Oct 2014

Preston Wake: Zeta values, periods and motives

We all learned in calculus class that the sum of the reciprocals of all the squares converges. But what is the actual value? Euler, in 1735, found that the answer is $\frac{\pi^2}{6}$. We probably also all learned this at some point, but, in retrospect, doesn’t it seem kind of crazy? I mean, we just did some random limit thingy, so it makes sense that the answer is transcendental, but why is it a transcendental number that we’ve heard of before? If transcendental numbers are so populous, how come we only ever see a few of them?

22 Oct 2014

Bena Tshishiku: Holler if ya sphere me

Okay, go cray, peeps here’s the deal. This week I’ma speak on vector fields On spheres — not clear how many fit when we ask them to be independent

15 Oct 2014

Andrew Geng: What is a quasicrystal?

The crystallographic restriction theorem says a finite-order automorphism of $\mathbb{Z}^3$ (in chemistry language, a symmetry of a crystal) has order $1$, $2$, $3$, $4$, or $6$. But $\mathbb{Z}^3$ is small potatoes; so let’s go to $\mathbb{Z}^n$, do some Galois theory in cyclotomic fields, and get us some icosahedral symmetry! (Icosahedrite is a real thing, say serious scientists.) Pretty pictures will be provided, including demonstrations of self-similarity. Self-similarity is always cool, right?

8 Oct 2014

Sean Howe: You can’t hear the shape of a Galois representation

As any musician knows, you can hear the shape of a string — for a fixed material and tension, the fundamental frequency uniquely determines the length. As any musician also knows, drummers aren’t musicians (it’s ok — neither am I!). That’s probably because you can’t hear the shape of a drum. Are mathematicians musicians? Certainly not geometers — it turns out you can’t hear the shape of a hyperbolic surface either. What about number theorists? With trace formulas, eigenvalues, length spectra and more, find out the answer this week at PIZZA SEMINAR!

1 Oct 2014

Yiwen Zhou: Solving polynomials $\mod p$

I will present the fact that for any polynomial $f$ of integer coefficients of degree grater than $1$, if $f$ is irreducible in $Q[x]$, than there are infinitely many prime numbers $p$ such that $f$ has no solution in $F_p$. Moreover, I will show that these prime numbers have positive natural density. As an example, I will compute the number of solutions of $x^3-x-1$ in $F_p$ for various $p$ and then relate these numbers to the coefficients of the $q$-expansion of a particular modular form.

4 Jun 2014

Masoud Kamgarpour: The Job Hunt

I graduated from University of Chicago in 2008. My advisor was Drinfeld. I am currently a faculty member in Australia. I am visiting UChicago to talk about job hunting for mathematics students. I did my studies/postdocs in four different countries: Canada, USA, Germany, and Australia. I am familiar with the advantages and disadvantages of each. I had a lot of ups and downs in my career, but ended up with a job that I love. In addition, I am quite familiar with the attitudes of UChicago students regarding job market, etc. I am hoping that sharing my experience will help fellow UChicago graduate students plan their future better.

28 May 2014

Annual AWM Postdoc Panel

Postdocs Agnes Beaudry, Hung Vinh Tran, Ronen Mukamel, and Davide A. Reduzzi will share their wisdom about the job search process, adjusting to being a postdoc, and life after the postdoc. This is a great opportunity for both younger grad students and those nearing graduation to learn about the academic career path, and to get their questions answered.

21 May 2014

Valia Gazaki: Impossibility theorems for indefinite integrals

We all know that the real function $e^{-x^2}$ does not have “an elementary antiderivative”. Other non elementary integrals are the famous elliptic integrals. But what does it mean to be non elementary? In this talk, we will define what it means to be integrated in elementary terms and give two criteria for a function not to have an elementary antiderivative. We will use these to prove that $\int e^{-x^2}\,dx$ is not an elemantary integral. All we will need is a little bit of field theory and complex analysis.

14 May 2014

Raluca Havarneanu: The Grothendieck–Riemann–Roch Theorem

I will explain Grothendieck’s approach to proving the theorem for a proper morphism between two quasi-projective varieties over a field.

7 May 2014

I will explain the phenomenon of orbit shadowing in hyperbolic dynamics with an example.

30 Apr 2014

Ben Fehrman: Bring The Noise

We’ll discuss how to describe systems which admit no description. At least not that I’d screw with. Not in this lifetime. Give up and frown upon Brownian motion. Derive Ito’s formula, aka the fundamental theorem of stochastic calculus, aka flex mcnasty, aka the 37th chamber, and affix a precise intuition to its mystical reality. Finally, describe the connection between differential equations and stochastic processes, better understand the processes and recall the beginning.

23 Apr 2014

Max Engelstein: Can you hear the shape of a … windchime? Xylophone?

The interplay between functional analysis and geometry is a rich subject which has produced some of the crown jewels of 20th century mathematics. But I don’t like the word “bundle”, so we will do spectral graph theory instead. There will be pictures of graphs, analysis without deltas or epsilons and some hand-waving towards big fancy theorems at the end.

16 Apr 2014

Sergei Sagatov: Classical Mechanics and Symplectic Geometry

We explain via the canonical formalism of Hamilton why symplectic geometry is the natural mathematical framework for classical mechanics and prove a classical result of Noether relating symmetries and conserved quantities.

9 Apr 2014

Tori Akin: Dictatorships disguised as democracies

A cute application of ultrafilters.

2 Apr 2014

Bena Tshishiku: Shocking Card Trick Revealed!

Mathematician stuns audience with magic trick. What happens next will surprise you!

12 Mar 2014

Henry Scher: Supersymmetry — a graphical representation

Ever wanted to learn what supersymmetry is really all about? Well, this isn’t really going to explain it, but it’s going to give you just enough that you can pretend to! We’ll start with a pseudo-explanation of quantum mechanics, turn to supersymmetry, and end up with the concept of adinkras.

All material beyond quantum mechanics comes from papers by Sylvester James Gates.

5 Mar 2014

Jonathan Wang: Number theory in real life — algebraic curves and codes

Error correcting codes are used when transmitting messages through noisy channels. For example, the ISBN is a code consisting of nine digits $a_i$ followed by a digit 0–9 or X corresponding to $\sum_i a_i \pmod{11}$. I will start by giving the definition of a code and proceed to give a few examples, including the binary Hamming code, which will be constructed using polynomials over a finite field. The Hamming code turns out to be an example of a Goppa code. These latter codes are constructed using linear systems on curves over finite fields. It turns out that curves with many rational points relative to their genus give rise to good codes. The Riemann Hypothesis gives a preliminary bound on the number of rational points for curves of fixed genus. Other bounds are discussed, and we will see how class field theory helps us come up with “good” codes.

Short version: see some cool arithmetic geometry applied to [a layman’s] real life. Get some ideas for what to write in your next NSF grant.

26 Feb 2014

Henry Chan: When finite spaces met homotopy theory

Have you seen a finite topological space? If so, do you know that they can have infinitely many non-trivial homotopy groups? Buckle up, because these spaces are gonna be legend … wait for it …

19 Feb 2014

Tianqi Fan: Zariski’s main theorem

This is an introduction to Zariski’s main theorem.

12 Feb 2014

Daniel Studenmund: Theorem? I Hardly Know ’Em!

We’ve all heard of the Four Color Theorem. Blah blah longstanding open problem blah blah computer-assisted proof blah. But did you know that it is equivalent to the fact that every snark is non-planar? (If so, you’d better bring some reading material.) This talk will cover some basic coloring problems in graph theory with a topological slant.

5 Feb 2014

Paul Apisa: The Icosahedral Solution to the Quintic

It’s one of those truly galling things to hear: Klein solved the quintic with an icosahedron in 1884. It makes it sound like Klein was playing D&D; in the basement of Gottingen when suddenly he glanced at the die and chuckled “My God, of course that’s how it’s done!”

We’ll start by talking about classifying $3$-manifolds by their fundamental groups, content ourselves with the finite fundamental group case, realize that we’ve stumbled into an ADE classification, then use some uber-classical algebraic geometry (Segre embedding, doubly ruled quadrics) to reduce solving the quintic to things we’ve serendipitously just discussed + the computation of some polynomial invariants. As per math talk etiquette, I will not compute in public.

29 Jan 2014

Sean Howe: Hyperbol(e)ic Number Theory

The number $x^2 + x + 41$ is prime for all $x$! Hyperbolic manifolds have no rational points! A million proofs that there are no imaginary quadratic fields of class number $1$! Unravel these mysteries, and more, this week at *drumroll* *cartwheels* *lion taming* PIZZA SEMINAR!

22 Jan 2014

Katie Mann: The Schwarzian Derivative

The Schwarzian is a terrible looking formula but actually a beautiful piece of math. Come find out why I (geometer, general-calculus-hater-at-large) think it’s a delightful idea to spend a whole hour talking about something that involves third derivatives.

This talk starts with words like “what are the isometries of the circle?” and ends with words like “cocycle on the Virasoro lie algebra of smooth vector fields” and “complex structure on Teichmuller space”. In the middle, we’ll see some classical projective geometry (turns out that shit is really cool!) and a few other surprises.

15 Jan 2014

Preston Wake: Sums of squares

Given positive integers $n$ and $k$, in how many ways can you write $n$ as the sum of $k$ squares? Looks like a simple enough question, but looks can be deceiving. We’ll discuss some cases of this question and we’ll see some of these pizza-seminar favourites come up: generating functions, class field theory, $L$-functions, quaternions, Fourier transforms, trace formulas, congruence subgroups, modular forms, Riemann–Roch, that picture of the upper-half plane tiled by semi-circle-triangles that everyone always draws, and more!

8 Jan 2014

Jenny Wilson: Generating functions

Despite their elementary foundations, generating functions are amazingly useful tools — with uses like solving recurrence relations, studying sequences’ asymptotics, computing statistics, and proving combinatorial identities. In this talk we’ll see some applications to binomial relations, symmetric group combinatorics, and random walks. There will be an overview of the basic theory for those who want a refresher, and some challenge problems for the more advanced.

4 Dec 2013

Weiyan Chen: Model Theory and Algebra

Often times after a theorem about the complex numbers is proven in a book, a seemingly innocent claim follows: “the result holds equally well for arbitrary algebraically closed field of characteristic zero”. What if the proof uses structures of $\mathbb{C}$ other than being a field (e.g. uses topology or complex analysis)? In this talk, I will talk about the Lefschetz principle which justifies such a statement. This new perspective viewing algebraic objects, quite unexpectedly, comes from logic, or more precisely, model theory.

27 Nov 2013

Subhadip Chowdhury: Cut-Copy-Paste — Algebra and Tiling

There is a long tradition when resolution of geometric questions requires us to depart the world of geometry and enlist the help of algebra. The oldest go back to the Greeks who were concerned with trisecting angles and constructing squares of equal area to a circle! Coming back to the present, we want to consider problems of the following nature:
“If a chessboard is covered by $21$ blocks of size $1 \times 3$, what are the possible locations for the remaining square?”
“Is it possible to tile a square with an odd number of triangles, all of which have the same area?”

As it turns out, the first one ends up being settled with the aid of the group ring and cyclotomic fields, and the second one leads us to call on valuation theory and Sperner’s lemma. In the upcoming talk, we will discuss some of the algebraic methods used to solve such tiling and related problems.

20 Nov 2013

Mary He: Symplectic Lefschetz Fibrations

In this talk, I will explain the connections between Lefschetz fibrations, symplectic $4$-manifolds and mapping class groups. In particular, I will talk about monodromies of symplectic Lefschetz fibrations and factorizations in mapping class groups, and survey some classification results on low-genus Lefschetz fibrations. If time permits, I will present an example due to D. Auroux which suggests a new approach to distinguish homeomorphic surfaces of general type.

13 Nov 2013

Fedor Manin: How to find mistakes in your dictionary

Have you ever wondered how Google Translate works? Well, that’s still a secret. But earlier this year researchers at the Googleplex published several papers on the arxiv in which they mapped words to a high-dimensional vector space and used linear transformations to translate between English-space and, say, Czech-space. Maybe linear algebra won’t supplant the sophisticated statistical models anytime soon, but the authors are shopping it at least as a quick way of scanning dictionaries for questionable entries. Come find out what happens when you project the numbers 1 through 5 onto a plane, and a bit about how neural networks work.

6 Nov 2013