# Department of Mathematics

## Featured Events

• #### Sylvia Serfaty (Courant Institute) colloquium at 3pm on Wednesday, October 17, 2018 in Eckhart 206

The title of the colloquium is "Systems of points with Coulomb interactions". Large ensembles of points with Coulomb interactions arise in various settings of condensed matter physics, classical and quantum mechanics, statistical mechanics, random matrices and even approximation theory, and they give rise to a variety of questions pertaining to analysis, Partial Differential Equations and probability. We will first review these motivations, then present the ''mean-field'' derivation of effective models and equations describing the system at the macroscopic scale. We then explain how to analyze the next order behavior, giving information on the configurations at the microscopic level and connecting with crystallization questions, and finish with the description of the effect of temperature.

• #### Anna Gilbert (University of Michigan) colloquium at 3pm on Monday, October 22, 2018 in Ryerson 251

In this talk, I will give two vignettes on the theme of sparse matrices in sparse analysis. The first vignette covers work from compressive sensing in which we want to design sparse matrices (i.e., matrices with few non-zero entries) that we use to (linearly) sense or measure compressible signals. We also design algorithms such that, from these measurements and these matrices, we can efficiently recover a compressed, or sparse, representation of the sensed data. I will discuss the role of expander graphs and error correcting codes in these designs and applications to high throughput biological screens. The second vignette flips the theme; suppose we are given a distance or similarity matrix for a data set that is corrupted in some fashion, find a sparse correction or repair to the distance matrix so as to ensure the corrected distances come from a metric; i.e., repair as few entries as possible in the matrix so that we have a metric. I will discuss generalizations to graph metrics, applications to (and from) metric embeddings, and algorithms for variations of this problem. I will also touch upon applications in machine learning and bio-informatics.

• #### Angus Macintyre (University of Edinburgh) colloquium at 3pm on Monday, October 29, 2018 in Ryerson 251

In 2005 Boris Zilber published a very influential paper, giving a sophisticated model-theoretic construction of an exponential field satisfying Schanuel's Conjecture and a kind of Nullstellensatz relating to extensions preserving a dimension arising from Schanuel's Conjecture. He proved some very remarkable properties of such exponential fields, and boldly conjectured that the classical complex exponential field is one of these fields. The conjecture of course assumes that Schanuel's Conjecture is true for the complex exponential, and subsequent research has generally made this assumption

• #### Patrick Billingsley lecture in probability, Allan Sly (Princeton University) on Thursday, November 8, 2018 at 4:00 pm in Kent 120

Phase Transitions of Random Constraint Satisfaction Problems. Random constraint satisfaction problems encode many interesting questions in the study of random graphs such as the chromatic and independence numbers. Ideas from statistical physics provide a detailed description of phase transitions and properties of these models. We will discuss the one step replica symmetry breaking transition that many such models undergo.

• #### Nalini Anantharaman (IRMA, University of Strasbourg, France) Zygmund-Calderon lectures on November 12 and 13

A hundred years ago, Einstein wondered about quantization conditions for classically ergodic systems. His 1917 paper may be considered to be the starting point of the field of quantum chaos''. Although a mathematical description of the spectrum of Schrödinger operators associated to ergodic classical dynamics is still missing, a lot of progress has been made on the delocalization of the associated eigenfunctions.

## News and Announcements

• #### André Neves named as Simons Investigator (Jul 9, 2018)

André Neves is one of three mathematicians who have been named as 2018 Simons Investigators.  These awards are for five years, and provide \$100,000 per year.

• #### 2018 PSD and Departmental Teaching Prizes Awarded (May 18, 2018)

Please join us in congratulating all of the graduate students who have earned teaching awards this year! The recipients of Lawrence and Josephine Graves Prize for excellence in undergraduate teaching for 2018 are Mathilde Gerbelli-Gauthier, Yu Li, and Karl Schaeffer, and the Physical Sciences Collegiate Division Prize for excellence in undergraduate teaching for 2018 has been awarded to Benjamin O'Connor.

• #### 2018 Wolf Prize in Mathematics (Feb 12, 2018)

We're happy to be able to share the news that Sasha Beilinson and Volodya Drinfeld have won the 2018 Wolf Prize in Mathematics. Please join us in congratulating them!

• #### Welcome to the department (Jan 19, 2018)

We are happy to welcome Eduard Looijinga, Pierre-Louis Lions, and Leonid Polterovich to our department.  Eduard will be here for all of Winter and Spring quarters, Pierre-Louis from 1/1 till 2/2, and Leonid from 1/21 till 2/24.  Thank you all for coming!