# Techmath - Math Seminars in Israel

*Abstract:*

Let X be a random variable defined by X = sum_i a_i x_i where x_i are independent random variables uniformly distributed in {-1, 1}, and a_i are real numbers. We investigate the tail behavior of the variable X, and apply the results to study associated linear threshold functions f:{-1,1}^n→{0,1}, which are indicators of events of the form {sum a_i x_i > t} for real numbers t. A puzzle: Let a = max_i |a_i| and assume sum a_i^2 = 1. Is it true that Pr[|X| <= a] > a/10 ? Joint work with Nathan Keller.

*Abstract:*

Being fractionally Calabi-Yau is a periodicity property of triangulated categories introduced by Kontsevich more than 20 years ago. It is quite rare that a finite-dimensional algebra has derived category of modules which is fractionally Calabi-Yau, nevertheless it is conjectured that for many posets (partially ordered sets) arising in algebraic combinatorics, their incidence algebras do have this property. Viewing posets as finite topological spaces, one can speak on their stratifications. I will explain how certain stratifications give rise to derived equivalences between the incidence algebra of a given poset and other algebras which are quotients of incidence algebras. We use this result to establish the fractionally Calabi-Yau property for a large family of posets of partitions. In addition, we achieve significant progress towards proving a conjecture of Chapoton concerning the equivalences of the derived categories of posets of Dyck paths and the Tamari lattices. Joint work with F. Chapoton and B. Rognerud.

*Abstract:*

The classical Severi problem is to show that the space of reduced and irreducible plane curves of fixed geometric genus and degree is irreducible. In case of characteristic zero, this longstanding problem was settled by Harris in 1986. In the first part of my talk I will give a brief overview of the ideas involved. Then I will describe a tropical approach to studying degenerations of plane curves, which is the main ingredient to a new proof of irreducibility obtained in collaboration with Xiang He and Ilya Tyomkin. The main feature of the construction is that it works in positive characteristic, where the other known techniques fail.

*Announcement:*

You are invited to a:

** Distinguished Lecture Series by**

**Prof. David Jerison (MIT)**

**Abstracts**:

In Lecture 2 we will discuss how methods from geometric measure theory and elliptic regularity theory (developed for minimal surfaces) apply to level sets. We will focus on a version of the Harnack inequality that tells us how level surfaces influence each other. This gets us part way towards understanding hot spots.

**THE LECTURE WILL BE AT 16:30 AND NOT AT 15:30 AS INDICATED IN THE POSTER**

All lectures will be in Amado 232.

Light refreshments will be given in the faculty lounge on the 8th floor.

*Announcement:*

You are invited to take part in the:

**Mathematical-Physics Seminar**

January 23rd, 2020

**If you want to take part in this event, click here**

**Schedule**:

10:20-10:45: Gathering, coffee & light refreshments on the 8th floor

10:45-11:45: **Uzy Smilansky (Weizmann)**

11:45-12:45: Lunch on the 8th floor

12:45-13:45: **Barry Simon (Caltech)**

13:45-14:00: break

14:00-15:00: **Percy Deift (NYU)**

15:00-15:30: Coffe & light refreshments on the 8th floor

15:30-16:30: **David Jerison (MIT)**

**For titles and abstracts, please go to: https://cms-math.net.technion.ac.il/mathematical-physics-seminar/ **

*Abstract:*

Let M be an orientable hyperbolic surface without boundary and let c be a closed geodesic in M. We prove that any side of any triangle formed by distinct lifts of c in the hyperbolic plane is shorter than c.

The talk will be presented for advanced undergraduate and beginning graduate students.

*Announcement:*

You are invited to a:

** Distinguished Lecture Series by**

**Prof. David Jerison (MIT)**

**Abstracts**:

In Lecture 3 we will explain how complex analysis and differential geometry, in particularas developed for minimal surface theory, can be used to characterize global solutions andprove rigidity and regularity results for free boundaries. This gives further insights into themissing ingredients that will be needed to understand level sets of eigenfunctions.

All lectures will be in Amado 232.

Light refreshments will be given in the faculty lounge on the 8th floor.

*Abstract:*

The profinite completion of a free profinite group on infinite set of generators is a profinite group of grater rank. However, it is still unknown whether it is a free profinite group too. I am going to present some partial results regarding to this question.

*Abstract:*

Let G be a group acting on a space X. A natural question to study is the asymptotical behavior of orbits when elements are chosen using some law.

We first look into a specific lattice in SL(2,R) acting on the real projective line when elements are chosen using a certain word norm, and show connections to the Minkowski question mark function, continued fractions and the stationary measure of a closely related random walk.

We then study the random walk on the real plane, generated by action of subgroups in SL(2,R). By applying carefully chosen scaling suggested by Maucourant and using a recent result of Benoist-Quint we reach a reasonable candidate for solution.

*Abstract:*

10:30-11:20 Shachar Carmeli - Goodwillie Calculus 11:30-12:20 Surojit Ghosh - Equivariant stable homotopy theory 13:50-14:40 Elhanan Nafha - Lie Algebra Models for Unstable Homotopy 14:50-15:40 Nicholas Meadows - Grothendieck Duality via Homotopy Theory 16:10-18:0 Shauly Ragimov - Moduli Spaces of Manifolds 17:10-18:00 Dimitar Kodjabachev - Tensor Triangulated Categories

*Announcement:*

You are cordially invited to:

** the 33 ^{rd} **

**Elisha Netanyahu Memorial Lecture**

**Professor ****Claire Voisin**

**College de France, France**

**Title**: *Hodge structures in algebraic geometry*

**Abstract**:

Hodge structures of weight 1 appear implicitly in the study of Riemann surfaces and their Jacobians, which are associated complex tori. In higher weight (degree, dimension), the theory of Hodge structures has been developed by Griffiths starting from the Hodge decomposition theorem.

I will explain what a Hodge structure is and how it can be used to study the geometry of algebraic varieties (or Kähler manifolds).

**Reception will be held at 16:30 in the Faculty Lounge Amado Mathematics Building, 8th Floor.**

*Abstract:*

After summarizing 1D periodic Jacobi matrices, I will define periodic Jacobi matrices on infinite trees. I'll discuss the few known results and some interesting examples and then discuss lots and lots of interesting conjectures. This is joint work mainly with Nir Avni and Jonathan Breuer but also with Jacob Christensen, Gil Kilai and Maxim Zinchenko.

It is on the spectral theory of a class of operators on trees, for which there has been literature on the random case even in the theoretical physics literature but I am not aware of any application to anything close to real physics so this is probably better as a math talk but I leave it to you to sort it out if you are interested. I don’t care at all which it is called or even if it is jointly sponsored.