Gal Porat

About

I am a number theorist interested in Galois representations and arithmetic geometry.

My email is galporat1"at"gmail.com.

Papers and Preprints

Solid locally analytic representations in mixed characteristic. 

In preparation.

Locally analytic vectors and decompletion in mixed characteristic.

To appear in Forum of Mathematics, Sigma.

Overconvergence of étale (φ,Γ)-modules in families. 

Appeared in Compositio Mathematica, 161(3), (2025), 555-593.

Locally analytic vector bundles on the Fargues-Fontaine curve.

Appeared in Algebra & Number Theory, vol. 18(5) (2024), 899-946. 

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

Appeared in Israel J. of Mathematics, vol. 249 (2022), 431-476.

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

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

Notes from talks

The following are notes of talks I gave in various seminars.

Lecture notes on the Emerton-Gee stack.  These are lectures notes for the second half of a course given in the the Kazhdan Sunday seminar in 

the Hebrew University of Jerusalem in the Spring semester of 2025. The first half was given by Ehud de-Shalit.  

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). 

Overconvergent modular forms and the Fontaine-Mazur conjecture. These are notes for my topic exam in the University of Chicago as a second year PhD student.

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