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Abstract:
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The Verjosky conjecture states that every codimension one Anosov flow in dimensions 4 or higher is orbitally equivalent to a suspension Anosov flow. Codimension one means that either the weak stable or weak unstable foliation is codimension one. This conjecture is 50 years old. In joint work with K. Mann and R. Potrie we construct
infinitely many counterexamples to the conjecture in 4-manifolds. To achieve that we  need a closed hyperbolic 3-manifold M, a faithful minimal representation of \pi_1(M) into Homeo^+(S^1) (the circle), and a group equivariant Cannon-Thurston map from S^1 to the sphere at infinity of hyperbolic 3-space. This allows to construct a topological Anosov flow in dimension 4, and we are able to construct a C^1 model from this flow.
Updated on Apr 22, 2026 09:45 AM PDT
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By the works of Kleiner-Leeb or Quint, we know that the only convex cocompact Zariski dense subgroups of a simple higher rank Lie group are cocompact lattices. I will talk about a dynamical analogue of this result which states that Zariski dense subgroups with a finite Bowen-Margulis-Sullivan measure are lattices. The argument relies on entropy rigidity techniques developed by Einsiedler-Katok and Lindenstrauss and offers a new strategy of showing that a discrete subgroup of a higher rank group is a lattice. Based on joint work with Minju Lee.
Updated on Apr 24, 2026 08:29 AM PDT
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In this talk I will discuss existence, uniqueness, and ergodicity results for Patterson-Sullivan measures on the Furstenberg boundary under arbitrary Anosov conditions. Previously a theory of such measures for Anosov groups has been successfully developed for measures supported on the partial flag manifold associated to the Anosov condition, which coincides with the Furstenberg boundary only under the strongest Anosov condition, Borel Anosov.
I will also discuss one of the key tools we develop: a new sufficient condition for the existence of a measurable boundary map associated to a Zariski dense representation. This boundary map result also applies to mapping class groups and discrete subgroups of the isometry groups of Gromov hyperbolic spaces.
This is joint work with Dongryul Kim.
Updated on Apr 23, 2026 02:58 PM PDT
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This seminar series will take place on UC Berkeley campus, in Evans Hall room 939.
We will discuss various results about embedding the figure eight knot complement into higher dimensional spaces, including hyperbolic and complex hyperbolic spaces and mapping class groups.
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This seminar series will take place on UC Berkeley campus, in Evans Hall room 740.
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This seminar series will take place on UC Berkeley campus, in Evans Hall room 939.
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This seminar series will take place on UC Berkeley campus, in Evans Hall room 740.
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This seminar series will take place on UC Berkeley campus, in Evans Hall room 939.
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This seminar series will take place on UC Berkeley campus, in Evans Hall room 740.
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You are cordially invited to attend our End-of-Semester potluck on Wednesday, May 13th from 5:00-7:00pm. We encourage you to bring your family or a guest---the more the merrier!
For those of you who do not know, a 'potluck' party is one in which the food is provided by YOU.  You prepare a dish, such as a salad, a main dish, or a dessert, bringing enough for yourself, your family/guests, and 4 more.  This way, everyone can have a little of each dish.  SLMath will provide beverages.
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This seminar series will take place on UC Berkeley campus, in Evans Hall room 740.
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No upcoming events under African Diaspora Joint Mathematics Workshop
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