# Gal Porat

### About me

I am a fourth year graduate student in mathematics at the University of Chicago.

My advisor is Matthew Emerton, and my main interests are algebraic number theory and arithmetic geometry.

Previously, I was an undergraduate and a Masters student at the Hebrew University of Jerusalem, studying under the supervision of Ehud de Shalit.

Here is a copy of my CV.

### Papers and Preprints

Lubin-Tate theory and overconvergent Hilbert modular forms of low weight.

To appear in Israel Journal of Mathematics.

(with Ehud de Shalit) Induction and restriction of (φ,Γ)-modules.

Appeared in Muenster J. Math., vol. 12 (2019), 215-237.
### Topic Proposal

During the second year of the PhD studies at the University of Chicago, students are required to give an expository presentation in some field of mathematics.

Here is my expository paper on work of Kisin: Overconvergent modular forms and the Fontaine-Mazur conjecture.
### Seminars organized

Modularity lifting student seminar in the University of Chicago, autumn 2020.
Shimura varieties student seminar in the university of Chicago, summer 2021.
### Seminar notes

These are notes of talks I gave in various seminars.
Computing the (phi,gamma)-module attached to a crystalline Kummer extension (number theory student seminar in the University of Chicago)
Eigenforms and trianguline representations (number theory student seminar in the University of Chicago)
The Sprague-Grundy theorem (Talk for the undergraduate math club)
Fibered categories and stacks (student seminar on stacks in the university of Chicago)
Modularity lifting for GL2 (Modularity lifting student seminar in the University of Chicago)
Attaching Galois representations to modular forms (after Deligne) (number theory student seminar in the University of Chicago)
Modularity lifting theorems and the case of GL1 (Modularity lifting student seminar in the University of Chicago)
The Method of Sen (number theory student seminar in the University of Chicago)
Adic Spaces (Fontaine-Fargues curve student seminar in the University of Chicago)
The Riemann-Roch Theorem (algebraic curves student seminar in the University of Chicago)
The Method of Chabauty and Coleman (number theory student seminar in the University of Chicago)
Etale (φ,Γ)-modules and Overconvergence (p-adic Hodge theory learning seminar in the University of Chicago)
Lubin-Tate Theory (number theory student seminar in the University of Chicago)
Group presentations and p-adic analytic groups (group theory seminar in the Hebrew University)
Tate's Isogeny Theorem (elliptic curves student seminar in the Hebrew Univeristy)
Asymptotically uniform period distribution (number theory seminar in Tel Aviv University)
Congruent numbers and elliptic curves (graduate student seminar in the Hebrew University)
### Other notes

The following notes are expository or miscellaneous notes that I wrote in Tex at some point in time for some reason or another.

These notes which are expository are usually much less comprehensive than other existing sources. Rather, the point was often to work out simple examples which are not so easy to find in the literature as a nonexpert.

For the most part they are not carefully written, so use them at your own risk (but please do let me know if you find any mistakes).
The p-adic Simpson Correspondence for rigid analytic varieties
Geometric description of rings appearing in p-adic Hodge theory
Completed Cohomology
Basic Examples and Computations in p-adic Hodge Theory
Galois Deformations
Basic Deformation Theory
Lubin-Tate characters are crystalline
Structure of the Hecke algebra for GL2
Galois Extensions and Galois Cohomology
Relating fields of norms associated with a finite unramified extension
Kahler Differentials of Inseparable Field Extensions
A Cayley-Hamilton type theorem whose proof uses commutative algebra