PRO (Presenting Results of Others) Seminar Ical Atom

The PRO Seminar is a weekly departmental forum dedicated to exploring mathematical developments, sharing influential articles, and discussing diverse topics of interest. The seminar provides a platform for researchers and students to present the work of others, fostering a collaborative environment for learning and academic growth.

Participation & Scheduling We use a shared Google Sheet to manage the seminar schedule. You can use this link to see upcoming talks or to sign up to present a topic or paper:

PRO Seminar Coordination & Sign-up Sheet

Contact The seminar is organized by Nadav Kalma. For questions or further information, please reach out via email: kalmn@post.bgu.ac.il

The seminar meets on Thursdays, 10:00-11:00, in -101
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This Week

Amit Levinson-Sela

Groups acting on trees with Tits’ independence property (P) (By Colin D. Reid & Simon M. Smith)

Tits’ independence property (P) and geometric density are two properties a group action on a tree can have; Tits showed that the combination of these properties yields interesting simple groups. However, constructing and detecting these properties remained unclear. Burger and Mozes’s introduction of universal groups gave one rich “local-to-global” way to construct groups with (P) by defining their action locally around each vertex. I will present a paper by Colin Reid and Simon Smith which defines local action diagrams, greatly generalizing the Burger-Mozes construction. Local action diagrams turn out to completely classify groups with property (P), as well as to be able to detect geometric density and other global properties of group actions on trees.

Link to the paper: https://link.springer.com/article/10.1007/s00208-026-03412-w

2025–26–B meetings

Upcoming Meetings

Date
Title
Speaker
Abstract
Jun 4 Groups acting on trees with Tits’ independence property (P) (By Colin D. Reid & Simon M. Smith)Online Amit Levinson-Sela

Tits’ independence property (P) and geometric density are two properties a group action on a tree can have; Tits showed that the combination of these properties yields interesting simple groups. However, constructing and detecting these properties remained unclear. Burger and Mozes’s introduction of universal groups gave one rich “local-to-global” way to construct groups with (P) by defining their action locally around each vertex. I will present a paper by Colin Reid and Simon Smith which defines local action diagrams, greatly generalizing the Burger-Mozes construction. Local action diagrams turn out to completely classify groups with property (P), as well as to be able to detect geometric density and other global properties of group actions on trees.

Link to the paper: https://link.springer.com/article/10.1007/s00208-026-03412-w

Past Meetings

Date
Title
Speaker
Abstract
Apr 16, 9:30–11:00 Stationary random subgroups in negative curvature יאיר גלזנר (BGU)

Preprint of Ilya Gekhtman and Arie Levit “Stationary random subgtroups in negative curvatire”.
May 7 On Tychonoff Groups by R.I. Grigorchuk Yair Hartman (BGU)

Link to article
May 14, 9:30–11:00 “Topological reconstruction theorems over uncountable algebraically closed fields” by B. Castle and R. O’Gorman (not yet in arXiv)Online Assaf Hasson (BGU)

In a seminal series of works, culminating in the monumental “What Determines an Algebraic Variety?” János Kollár, Max Lieblich, Martin Olsson, and Will Sawin prove that a normal projective algebraic variety of dimension at least 2 over an uncountable field of characteristic 0 can be reconstructed, in a precise sense, solely from its underlying topological space. The results of KLOS are specific to char. 0 and to normal varieties. Castle and O’Gorman, using the model theoretic machinery of Zilber’s Restricted Trichotomy, extend these results to all quasi projective varieties (of dimension at least 2) in all characteristics, in the case where the underlying field is algebraically closed and uncountable. In the talk, I will present the results and try to sketch the strategy of proof of the new result.
May 28 Infinite volume and infinite injectivity radius (Mikolaj Fraczyk, Tsachik Gelander) Nadav Kalma (BGU)

In their paper, Frączyk and Gelander prove a conjecture by Margulis: for a higher-rank simple Lie group $G$, a discrete subgroup has an infinite injectivity radius if and only if it has infinite covolume. The novel methods used to resolve this rely on ergodic theory—specifically, analyzing random walks on the space of discrete subgroups, alongside new stiffness and rigidity results for these stationary measures. In this talk, I will introduce the foundational definitions and present an outline of the main arguments used to prove the conjecture.

Link to paper

Seminar run by Nadav Kalma