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Columbia Geometric Topology SeminarSpring 2024 

Organizers: Francesco Lin, Siddhi Krishna, Ross Akhmechet
The GT seminar typically meets on Fridays at 2:00pm Eastern time in Room 307, Mathematics Department, Columbia University.
Other area seminars. Our email list. Archive of previous semesters
Date  Time (Eastern)  Speaker  Title 

January 26 
3:30pm Eastern (note unusual time!) 
Bojun Zhao 
Coorientable taut foliations in Dehn fillings of pseudoAnosov mapping tori with coorientationreversing monodromy 
February 2 
3:30pm Eastern (note unusual time!)  Sebastian HurtadoSalazar 
Length functions on Lie groups and lattices 
February 9 
2pm Eastern 
Mike Willis 
Spectral JonesWenzl projectors and differences between Khovanov homology and stable homotopy 
February 16 
3:30pm Eastern (note unusual time!) 
Alex Zupan 
The square knot bounds infinitely many nonisotopic ribbon disks 
February 23 
2pm Eastern 
Sally Collins 
Homology cobordism & smooth knot concordance 
March 1 
2pm Eastern 
Eugen Rogozinnikov 
Parametrizing spaces of positive representations 
March 7 (Thursday) 
3pm Eastern (note unusual day and time!) 
Francesco Costantino 
Stated skein modules of 3manifolds and TQFTs 
March 8 
2pm Eastern 
Onkar Gujral 

March 15 
2pm Eastern 
no seminar 
Spring Break 
March 22 
2pm Eastern 
Emmanuel Wagner 

March 29 
2pm Eastern 
no seminar 
Simons Annual Meeting 
April 5 
2pm Eastern 
Emily Stark  
April 12 
2pm Eastern 
Ian Zemke 

April 19 
2pm Eastern  Henry Segerman 

April 26 
2pm Eastern  Patrick Orson 

April 30 (Tuesday) 
TBA  Bruno Martelli 

Bojun Zhao
Title: Coorientable taut foliations in Dehn fillings of pseudoAnosov mapping tori with coorientationreversing monodromy
Abstract: Let f be a pseudoAnosov homeomorphism on a compact orientable surface with nonempty boundary, such that f has a coorientable stable foliation and reverses the coorientation on it. Let M denote the mapping torus of f. In this talk, I will discuss some constructions of coorientable taut foliations in those Dehn fillings of M with filling multislopes constrained by a bound from the degeneracy loci on the boundary components of M. In certain cases where M has connected boundary and is Floer simple, we can construct coorientable taut foliations in all nonLspace Dehn fillings of M.
Sebastian HurtadoSalazar
Title: Length functions on Lie groups and lattices
Abstract: We will discuss the notion of a length function on a group, focusing on lattices in Lie groups, such as SL_n(Z), and discuss how techniques from dynamics can help to understand some important questions about these groups.
Mike Willis
Title: Spectral JonesWenzl projectors and differences between Khovanov homology and stable homotopy
Abstract: Categorified JonesWenzl projectors P_n are widely studied, with endomorphisms related to the Khovanov homology of torus links. We will discuss the lifts of such projectors to the category of spectra, focusing on certain properties of P_n that fail to lift. These are some of the first structural differences found between Khovanov homology and Khovanov stable homotopy, and include the surprising negative answer to a question of LawsonLipshitzSarkar asking whether topological Hochschild homology for tangle spectra can be used to define a spectral invariant for links in S1xS2. This work is joint with Matt Stoffregen.
Alex Zupan
Title: The square knot bounds infinitely many nonisotopic ribbon disks
Abstract: A knot K in S^3 is (smoothly) slice if K is the boundary of a properly embedded disk D in B^4, and K is ribbon if this disk can be realized without any local maxima with respect to the radial Morse function on B^4. In dimension three, a knot K with nice topology – that is, a fibered knot – bounds a unique fiber surface up to isotopy. Thus, it is natural to wonder whether this sort of simplicity could extend to the set of ribbon disks for K, arguably the simplest class of surfaces bounded by a knot in B^4. Surprisingly, we demonstrate that the square knot, one of the two nontrivial ribbon knots with the lowest crossing number, bounds infinitely many distinct ribbon disks up to isotopy. This is joint work with Jeffrey Meier.
Sally Collins
Title: Homology cobordism & smooth knot concordance
Abstract: The 0surgeries of two knots K1 and K2 are homology cobordant rel meridians if there exists an integer homology cobordism X between them such that the two positive knot meridians are in the same homology class of X. It is a natural question to ask: if two knots have 0surgeries related in this sense, must they be smoothly concordant? We give a pair of rationally slice knots as counterexample, and along the way expand upon an involutive knot Floer homology technique for obstructing torsion in the smooth concordance group first introduced by Hom, Kang, Park, and Stoffregen. No previous knowledge of Heegaard Floer theory will be assumed.
Eugen Rogozinnikov
Title:Parametrizing spaces of positive representations
Abstract: Higher Techmüller theory deals with spaces of representations of the fundamental group of a surface into a reductive Lie group $G$, modulo the conjugation, especially with the connected components (called higher Teichmüller spaces) that consist entirely of injective representations with discrete image.
Francesco Costantino
Title:Stated skein modules of 3manifolds and TQFTs
Abstract: After reviewing the definition of stated skein modules for surfaces and 3 manifolds, I will detail how this recent notion allows to relate topological constructions (related to cut and paste techniques) to algebraic ones (braided tensor products of algebra objects in braided categories for instance). I will explain how the stated skein algebra of some special surfaces provides a topological description for some notable algebras (e.g. the quantised functions ring $O_q(\mathfrak{sl_2})$ or its ``transmutation’’ BSL_2(q)). Then I will describe how stated skein moduli of 3manifolds fit into a TQFT framework albeit a non completely standard one. If time permits I will also discuss some unexpected non injectivity results in dimension 3. (Joint work with Thang Le)