הסמינר מתכנס בימי שלישי, בשעות 14:30-15:30, באולם -101

TBA

## מפגשים בסמסטר 23–2022–א

### המפגשים הבאים

תאריך
כותרת
מרצה
תקציר
6 בדצמ TBAOnline Dmitry Kerner (BGU)

TBA

13 בדצמ Random Manifolds and KnotsOnline Chaim Even Zohar (Technion)

We introduce a combinatorial method of generating random submanifolds of a given manifold in all dimensions and codimensions. The method is based on associating random colors to vertices, as in recent work by Sheffield and Yadin on curves in 3-space. We determine conditions on which submanifolds can arise in which ambient manifolds, and study the properties of random submanifolds that typically arise. In particular, we investigate the knotting of random curves in 3-manifolds, and discuss some other applications.

Joint work with Joel Hass

20 בדצמ TBAOnline Guy Salomon (Weizmann Institute)

TBA

3 בינו TBAOnline Tsviqa Lakrec (University of Zurich)

TBA

10 בינו TBAOnline Emanuel Milman (Technion)

TBA

### המפגשים הקודמים

תאריך
כותרת
מרצה
תקציר
25 באוק תב“ה Departamental meeting
8 בנוב Word maps and word measures: probability and geometry Itay Glazer (Northwestern University)

Given a word w in a free group F_r on a set of r elements (e.g. the commutator word w=xyx^(-1)y^(-1)), and a group G, one can associate a word map w:G^r–>G. For g in G, it is natural to ask whether the equation w(x1,…,xr)=g has a solution in G^r, and to estimate the ”size“ of this solution set, in a suitable sense. When G is finite, or more generally a compact group, this becomes a probabilistic problem of analyzing the distribution of w(x_1,…,x_r), for Haar-random elements x_1,…,x_r in G. When G is an algebraic group, such as SLn(C), it is natural to study the geometry of the fibers of w. Such problems have been extensively studied in the last few decades, in various settings such as finite simple groups, compact p-adic groups, compact Lie groups, simple algebraic groups, and arithmetic groups. Analogous problems have been studied for Lie algebra word maps as well. In this talk, I will mention some of these results, and explain the tight connections between the probabilistic and algebraic approaches.

Based on joint works with Yotam Hendel and Nir Avni.

15 בנוב Definably semisimple groups interpretable in p-adically closed fields (Joint work with Assaf Hasson and Ya‘acov Peterzil) Yatir Halevi (Haifa University)

Identifying and characterizing the groups and fields one can define in various first order structures has had multiple applications within model theory and in other branches of mathematics. We focus here on p-adically closed fields. Let K be a p-adically closed field (for example, Q_p). We will discuss some recent results regarding interpretable groups and interpretable fields in K:

1) Let G be an interpretable group. If G is definably semisimple (i.e. G has no definable infinite normal abelian subgroups) group, then there exists a finite normal subgroup H such that G/H is definably isomorphic to a K-linear group.

2) Let F be an interpretable field. Then F is definably isomorphic to a finite extension of K.

No knowledge in model theory will be assumed, but some basic knowledge in logic will help.

22 בנוב On classification of semigroups by algebraic, logical and topological tools Grigory Mashevitzky (BGU)

ההרצאה תתקיים לכבוד פרישתו לגמלאות של פרופ‘ גרגורי משביצקי.

29 בנוב Non-Rigidity of Horocycle Orbit Closures in Geometrically Infinite Surfaces Or Landesberg (Yale University)

Horospherical group actions on homogeneous spaces are famously known to be extremely rigid. In finite volume homogeneous spaces, it is a special case of Ratner’s theorems that all horospherical orbit closures are homogeneous. Rigidity further extends in rank-one to infinite volume but geometrically finite spaces. The geometrically infinite setting is far less understood.

We consider $\mathbb{Z}$-covers of compact hyperbolic surfaces and show that they support quite exotic horocycle orbit closures. Surprisingly, the topology of such orbit closures delicately depends on the choice of a hyperbolic metric on the covered compact surface. In particular, our constructions provide the first examples of geometrically infinite spaces where a complete description of horocycle orbit closures is known. Based on an ongoing joint work with James Farre and Yair Minsky.

סמינר מאורגן על-ידי ד“ר מיכאל ברנדנבורסקי