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Fall 2022
Date 
Time (Eastern) 
Speaker 
Title 
September 16

2pm

Amina Abdurrahman

A global cohomological formula for Reidemeister torsion

September 23

2pm

Jean Pierre Mutanguha 
Canonical forms for free group automorphisms

September 30

2pm

Marco Marengon

Relative genus bounds in indefinite 4manifolds

October 7

n.a.

no speaker

No seminar (Krichever Conference)

October 14

2pm

Marta Magnani

Parametrizing the space of maximal representations

October 21

2pm

Sam Taylor

Endperiodic maps via pseudoAnosov flows

October 28

2pm

Funda Gultepe

Curves, hexagons and geometry of surfaces

November 4

Double Header Pt 1 @ 2pm

Peter Feller

On the length of knots on a Heegaard surface of a 3manifold

November 4

Double Header Pt 2 @ 4:45pm

John Baldwin

Floer homology and nonfibered knots

November 11

2pm

Thang Nguyen

Marked length spectrum rigidity for relatively hyperbolic groups

November 18

2pm

Jane Wang

The topology of the moduli space of dilation surfaces

November 25

n.a.

no speaker

Happy Thanksgiving!

December 2

2pm

Katie Mann

Classifying Anosov flows on 3manifolds 
December 9

2pm

Gary Guth

Satellites, Stabilizations, and Exotic Surfaces 
Abstracts
September 16: Amina Abdurrahman (Stony Brook)
Title: A global cohomological formula for Reidemeister torsion
Abstract: We give a global cohomological formula for Reidemeister torsion of a 3manifold together with a symplectic local system. This can be considered as the topological analogue of a numbertheoretic formula generalizing a result of Deligne in the 70s about local espilon factors. We plan to tell the topological story and touch on some of the related ideas in topology and number theory.
September 23: Jean Pierre Mutanguha (Princeton)
Title: Canonical forms for free group automorphisms
Abstract: The Nielsen–Thurston theory of surface homeomorphisms can be thought of as a surface analogue to the Jordan Canonical Form. I will discuss my progress in developing a similar canonical form for free group automorphisms. (Un)Fortunately, free group automorphisms can have arbitrarily complicated behaviour. This is a significant barrier to translating arguments that worked for surfaces into the free group setting; nevertheless, the overall ideas/strategies do translate!
September 30: Marco Marengon (Renyi Institute)
Title: Relative genus bounds in indefinite 4manifolds
Abstract: Given a closed 4manifold X with an indefinite intersection form, we consider smoothly embedded surfaces in X − int(B^4), with boundary a given knot K in the 3sphere. We give several methods to bound the genus of such surfaces in a fixed homology class. Our techniques include adjunction inequalities from Heegaard Floer homology and the BauerFuruta invariants, and the 10/8 theorem. In particular, we present obstructions to a knot being Hslice (that is, bounding a nullhomologous disc) in a 4manifold and show that the set of Hslice knots can detect exotic smooth structures on closed 4manifolds. This is joint work with Ciprian Manolescu and Lisa Piccirillo.
October 14: Marta Magnani (Heidelberg)
Title: Parametrizing the space of maximal representations
Abstract: Higher rank Teichmüller theory was developed as a generalization of classical Teichmüller theory and is concerned with the study of representations of fundamental groups of oriented surface S of negative Euler characteristic into simple real Lie groups G of higher rank. In the talk we will introduce Higher rank Teichmüller theory with particular attention to maximal representations. We will then introduce the Siegel space and discuss how, given a hyperbolic surface with boundary, one can parametrize the space of maximal representations from the fundamental group of the surface into PSp(2n,R).
October 21: Sam Taylor (Temple)
Title: Endperiodic maps via pseudoAnosov flows
Abstract: We show that every atoroidal, endperiodic map of an infinitetype surface is isotopic to a homeomorphism that is naturally the first return map of a pseudoAnosov suspension flow on a fibered manifold. Morally, these maps are all obtained by “spinning” fibers around a surfaces in the boundary of the fibered cone. The structure associated to these spun pseudoAnosov maps allows for several applications. These include defining and characterizing stretch factors of endperiodic maps, relating Cantwell—Conlon foliation cones to Thurston’s fibered cones, and defining a convex entropy function on these cones that extends log(stretch factor). This is joint work with Michael Landry and Yair Minsky.
October 28: Funda Gultepe (Toledo)
Title: Curves, hexagons and geometry of surfaces
Abstract: In this talk, we define and study graphs associated to hexagon decompositions of surfaces by curves and arcs and relate them to pants graph and the mapping class group. We will also give an estimate on the diameter of the moduli space of hexagon decompositions on a surface. This is a joint work with Hugo Parlier.
November 4: Peter Feller (ETH Zurich)
Title: On the length of knots on a Heegaard surface of a 3manifold.
Abstract: 3manifold theory has expanded its tool box in recent decades: topological, (Floer and quantum) homological, and geometrical methods all have been employed with success. However, often the relation between these different approaches remains mysterious.
In this talk we explore connections between the topology and the geometry of 3manifolds by using Heegaardsplittings (topology) of a 3manifold to describe hyperbolic structures (geometry) on it. More concretely, for a knot K that lies on a Heegaard surface of a closed oriented connected 3manifold M, we describe a sufficient condition for M to carry a hyperbolic structure. Furthermore, whenever our criterion applies, we determine the length of K up to a multiplicative constant.
Upshot of our approach: there is NO Ricciflow machine running in the background. Instead, the motor behind what we do is an effective version of Thurston's hyperbolic Dehn surgery. Applications include a Ricciflow free proof of Mather's result that random 3manifolds (in the sense of DunfieldThurston) are hyperbolic, and bounds on the diameter and injectivity radius of a random 3manifold.
November 4: John Baldwin (Boston College)
Title: Floer homology and nonfibered knots
Abstract: A fundamental question for any knot invariant asks which knots it detects. For example, it is a famous open question whether the Jones polynomial detects the unknot. The detection question for knot Floer homology and the KhovanovRozansky link homology theories has received a lot of attention of the past two decades, culminating in proofs that these theories detect six knots: the unknot, the trefoils, the figure eight, and the cinquefoils. Crucial in each of these detection results (save for that of the unknot) is that the knot in question is fibered. I'll discuss recent work with Sivek in which we show for the first time that knot Floer homology and Khovanov homology can also detect nonfibered knots, and that HOMFLY homology can in fact detect infinitely many knots.
November 4: Thang Nguyen (Florida State)
Title: Marked length spectrum rigidity for relatively hyperbolic groups
Abstract: Burns and Katok asked, among homeomorphic manifolds of negative sectional curvature, whether the lengths of the family of marked geodesic loops determine the geometry of a manifold. I will state a coarse version of this question for finitely generated groups. After going over some previously known results, we'll focus our attention on the case of relatively hyperbolic groups. This is based on a joint work with Shi Wang.
November 18: Jane Wang (Maine)
Title: The topology of the moduli space of dilation surfaces
Abstract: Translation surfaces are geometric objects that can be defined as a collection of polygons with sides identified in parallel opposite pairs by translation, or as a Riemann surface together with a holomorphic oneform. If we generalize slightly and allow for polygons with sides identified by both translation and dilation, we get a new family of objects called dilation surfaces. While translation surfaces are wellstudied, much less is known about dynamics on dilation surfaces and their moduli spaces. In this talk, we will survey recent progress in understanding the topology of moduli spaces of dilation surfaces, including realizing the fundamental groups of these moduli spaces as certain subgroups of the mapping class group. This talk represents joint work with Paul Apisa and Matt Bainbridge.
December 2: Katie Mann (Cornell)
Title: Classifying Anosov flows on 3manifolds
Abstract: Anosov flows are rich examples of dynamical systems, they include the geodesic flows on unit tangent bundles of hyperbolic surfaces, and many other examples. This talk is about how dynamics, geometry and topology interact in dimension 3 via some longstanding open questions: Which 3manifolds support Anosov flows? Which 3manifolds support many topologically distinct Anosov flows? What invariants can be used to distinguish them? I will describe some of the state of the art, and recent work with Thomas Barthelmé, Steven Frankel, and Sergio Fenley that provides new topological invariants towards this classification problem.
December 9: Gary Guth (Oregon)
Title: Satellites, Stabilizations, and Exotic Surfaces
Abstract: A long standing question in the study of exotic behavior in dimension four is whether exotic behavior is “stable". For example, in thinking about the fourdimensional hcobordism theorem, Wall proved that simply connected, exotic fourmanifolds always become smoothly equivalent after applying a suitable stabilization operation enough times. Similarly, HosokawaKawauchi and BaykurSunukjian showed that exotic surfaces become smoothly equivalent after stabilizing the surfaces some number of times. The question remains, "how many stabilizations are necessary, and is one always enough?" By considering certain satellite operations, we provide an answer to this question in the case of exotic surfaces with boundary
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