Ical
https://mathematics.huji.ac.il/calendar?type=month&month=term
en<a href="https://mathematics.huji.ac.il/event/dynamics-lunch-michael-chapman?delta=0" >Dynamics Lunch: Michael Chapman ״Markoff triples״</a>
https://mathematics.huji.ac.il/event/dynamics-lunch-michael-chapman
Partially based on the paper "The Markoff Group of Transformations in Prime and Composite Moduli" by Meiri and Puder.Tue, 25 Jun 2019 09:00:00 +0000Anonymous83885 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/logic-seminar-tba?delta=0" >Logic Seminar - tba</a>
https://mathematics.huji.ac.il/event/logic-seminar-tba
Wed, 26 Jun 2019 08:00:00 +0000Anonymous80583 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/analysis-seminar-dvoretzky-lecture-assaf-naor?delta=0" >Analysis Seminar - Dvoretzky lecture - Assaf Naor "The (in)compatibility of 3 and 5 dimensional Heisenberg geometry with Lebesgue spaces"</a>
https://mathematics.huji.ac.il/event/analysis-seminar-dvoretzky-lecture-assaf-naor
Title: The (in)compatibility of 3 and 5 dimensional Heisenberg geometry with Lebesgue spaces
Abstract: The 3-dimensional (discrete) Heisenberg geometry is the shortest-path metric on the infinite graph whose vertex set is the integer grid $\Z^3$ and the neighbors of each integer vector $(a,b,c)$ are the four integer vectors $$(a+ 1,b,c), (a- 1,b,c), (a,b+ 1,c+ a), (a,b- 1,c- a).$$
Analogously, the $5$-dimensional (discrete) Heisenberg geometry is the shortest-path metric on the infinite graph whose vertex set is the integer grid $\Z^5$ and the neighbors of each integer vector $(a,b,c,d,e)$ are the eight integer vectors $(a\pm 1,b,c,d,e), (a,b\pm 1,c, d,e), (a,b ,c\pm 1,d, e\pm a), (a,b ,c,d\pm 1, e\pm b)$. The purpose of this talk is to describe the culmination of a multi-decade effort to understand the extent to which these metric spaces can be represented faithfully as subsets of an $L_p(\mu)$ space. It turns out that if $p>1$, then there is no qualitative difference between the answer to this question in dimensions $3$ and $5$. However, if $p=1$, then the behaviors of dimensions $3$ and $5$ diverge markedly. These results rely on several ideas and tools that were introduced over the years, and they relate deeply to a rich variety of mathematical disciplines. They answer major open questions in metric embeddings, Lipschitz factorization, dimension reduction, and semidefinite programming. We will describe key statements and ideas while highlighting the most recent step which introduces the notion of a foliated corona decomposition (joint work with Robert Young).
Despite the fact that our discussion is linked to a wide range of areas of mathematics, the talk is intended for a general audience of mathematicians and theoretical computer scientists. We will not rely on any prerequisites beyond an undergraduate degree in mathematics, and all of the relevant background will be introduced and explained.Wed, 26 Jun 2019 09:00:00 +0000Anonymous85556 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/minicourse-jared-weinstein-boston-university-geometrization-local-langlands-program-1?delta=0" >Minicourse: Jared Weinstein (Boston University "Geometrization of the local Langlands program"</a>
https://mathematics.huji.ac.il/event/minicourse-jared-weinstein-boston-university-geometrization-local-langlands-program-1
Prof. Jared Weinstein (Boston University) will give a series of 3 talks titled
"Geometrization of the local Langlands program"
Abstract: The Langlands program links automorphic forms and Galois representations (of a local or global field). In contrast, the geometric Langlands program takes a curve X over the complex numbers, and links the moduli space of rank n vector bundles on X to rank n local systems on X. A beautiful program initiated by Fargues reveals the unity of the two programs over the field of p-adic numbers. In this program, the role of X is played by the Fargues-Fontaine curve. The goal of this series of lectures is to understand Fargues' suite of conjectures. The conjectures are a theorem in the case of n = 1, where one recovers local class field theory in a new way.
Talk 1: The Fargues-Fontaine curve, Wednesday 26/6, 14-15:30
Talk 2: The stack of vector bundles, Sunday 31/6, 14-15:30
Talk 3: Statement of the conjectures, Monday 1/7, 14-15:30
All three talks will be held in Ross 70.Wed, 26 Jun 2019 11:00:00 +0000Anonymous86031 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/group-and-dynamics-seminar-asaf-naor-princeton?delta=0" >Group and dynamics seminar: Michael Chapman (HUJI): Cutoff on Ramanujan complexes</a>
https://mathematics.huji.ac.il/event/group-and-dynamics-seminar-asaf-naor-princeton
Abstract: A Markov chain over a finite state space is said to exhibit the total variation cutoff phenomenon if, starting from some Dirac measure, the total variation distance to the stationary distribution drops abruptly from near maximal to near zero. It is conjectured that simple random walks on the family of $k$-regular, transitive graphs with a two sided $\epsilon$ spectral gap exhibit total variation cutoff (for any fixed $k$ and $\epsilon). This is known to be true only in a small number of cases. In this talk we discuss a new family of such graphs that exhibit cutoff, namely the $1$-skeleton of Ramanujan complexes. This family is the first natural one -- occurring as Cayley graphs of $PGL(d, q)$ -- for which the cutoff point is at a non-optimal time. Joint work with Ori Parzanchevski.Thu, 27 Jun 2019 07:00:00 +0000Anonymous82733 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/groups-and-dynamics-seminar-asaf-katz-chicago-application-margulis-inequality-effective?delta=0" >Groups and Dynamics seminar: Asaf Katz (Chicago) - An application of Margulis' inequality to effective equidistribution.</a>
https://mathematics.huji.ac.il/event/groups-and-dynamics-seminar-asaf-katz-chicago-application-margulis-inequality-effective
<p style="font-family:Arial, Helvetica, sans-serif; font-size:small; background-color:rgb(255, 255, 255)">Abstract: <span style="font-family:arial, sans-serif">Ratner's celebrated equidistribution theorem states that the trajectory of any point in a homogeneous space under a unipotent flow is getting equidistributed with respect to some algebraic measure. In the case where the action is horospherical, one can deduce an effective equidistribution result by mixing methods, an idea that goes back to Margulis' thesis. When the homogeneous space is non-compact, one needs to impose further ``d</span><span style="font-family:arial, sans-serif">iophantine conditions'' over the base point, quantifying some recurrence rates, in order to get a quantified equidistribution result.</span><span style="font-family:arial, sans-serif"> </span></p><p style="font-family:Arial, Helvetica, sans-serif; font-size:small; background-color:rgb(255, 255, 255)">In the talk I will discuss certain diophantine conditions, and in particular I will show how a new Margulis' type inequality for translates of horospherical orbits helps verify such conditions, leading to a quantified equidistribution result for a large class of points, akin to the results of A. Strombergsson dealing with SL2 case. In particular we deduce a fully effective quantitative equidistribution statement for horospherical trajectories of lattices defined over number fields.</p>Thu, 27 Jun 2019 08:30:00 +0000Anonymous86451 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/colloquium?delta=0" >Colloquium Dvoretzky lecture: Assaf Naor(Princeton) - An average John theorem </a>
https://mathematics.huji.ac.il/event/colloquium
<br /><u>Abstract</u>: We will prove a sharp average-case variant of a classical embedding theorem of John through the theory of nonlinear spectral gaps. We will use this theorem to provide a new answer to questions of Johnson and Lindenstrauss (1983) and Bourgain (1985) on metric dimension reduction, and explain how it leads to algorithms for approximate nearest neighbor search.Thu, 27 Jun 2019 11:30:00 +0000Anonymous63603 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/basic-notions-hillel-furstenberg-huji-affine-convex-representations-and-harmonic-0?delta=0" >Basic Notions: Hillel Furstenberg (HUJI) : "Affine (Convex) representations and harmonic functions on symmetric spaces." Part 2</a>
https://mathematics.huji.ac.il/event/basic-notions-hillel-furstenberg-huji-affine-convex-representations-and-harmonic-0
Classical group representation theory deals with group actions on linear spaces; we consider group actions on compact convex spaces, preserving topological and convex structure. We focus on irreducible actions, and show that for a large class of groups - including connected Lie groups - these can be determined. There is a close connection between this and the theory of bounded harmonic functions on symmetric spaces and their boundary values. A remarkable phenomenon is the fact that for SL(2,R), up to isomorphism, there exists a unique non-degenerate irreducible affine representation.Thu, 27 Jun 2019 13:00:00 +0000Anonymous85982 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/minicourse-jared-weinstein-boston-university-geometrization-local-langlands-program-0?delta=0" >Minicourse: Jared Weinstein (Boston University "Geometrization of the local Langlands program"</a>
https://mathematics.huji.ac.il/event/minicourse-jared-weinstein-boston-university-geometrization-local-langlands-program-0
Prof. Jared Weinstein (Boston University) will give a series of 3 talks titled
"Geometrization of the local Langlands program"
Abstract: The Langlands program links automorphic forms and Galois representations (of a local or global field). In contrast, the geometric Langlands program takes a curve X over the complex numbers, and links the moduli space of rank n vector bundles on X to rank n local systems on X. A beautiful program initiated by Fargues reveals the unity of the two programs over the field of p-adic numbers. In this program, the role of X is played by the Fargues-Fontaine curve. The goal of this series of lectures is to understand Fargues' suite of conjectures. The conjectures are a theorem in the case of n = 1, where one recovers local class field theory in a new way.
Talk 1: The Fargues-Fontaine curve, Wednesday 26/6, 14-15:30
Talk 2: The stack of vector bundles, Sunday 31/6, 14-15:30
Talk 3: Statement of the conjectures, Monday 1/7, 14-15:30
All three talks will be held in Ross 70.Sun, 30 Jun 2019 11:00:00 +0000Anonymous86030 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/minicourse-jared-weinstein-boston-university-geometrization-local-langlands-program?delta=0" >Minicourse: Jared Weinstein (Boston University "Geometrization of the local Langlands program"</a>
https://mathematics.huji.ac.il/event/minicourse-jared-weinstein-boston-university-geometrization-local-langlands-program
Prof. Jared Weinstein (Boston University) will give a series of 3 talks titled
"Geometrization of the local Langlands program"
Abstract: The Langlands program links automorphic forms and Galois representations (of a local or global field). In contrast, the geometric Langlands program takes a curve X over the complex numbers, and links the moduli space of rank n vector bundles on X to rank n local systems on X. A beautiful program initiated by Fargues reveals the unity of the two programs over the field of p-adic numbers. In this program, the role of X is played by the Fargues-Fontaine curve. The goal of this series of lectures is to understand Fargues' suite of conjectures. The conjectures are a theorem in the case of n = 1, where one recovers local class field theory in a new way.
Talk 1: The Fargues-Fontaine curve, Wednesday 26/6, 14-15:30
Talk 2: The stack of vector bundles, Sunday 31/6, 14-15:30
Talk 3: Statement of the conjectures, Monday 1/7, 14-15:30
All three talks will be held in Ross 70.Mon, 01 Jul 2019 11:00:00 +0000Anonymous86029 at https://mathematics.huji.ac.il