# Math Calendar

### Upcoming Events

## On Isoperimetric Functions of Finitely Presented Groups

Alexander Olshanskiy, Vanderbilt University

Location: Stevenson 5211

The results recently obtained by Olshanskiy and Sapir solve two well-known problems about isoperimetric functions (or Dehn functions) of finitely presented groups. We have completed the description of the isoperimetric spectrum of finitely presented groups modulo $\bf NP=P$ hypothesis (a problem first proposed by M. Bridson in 1996), and we constructed a finitely presented group with quadratic isoperimetric functions and undecidable conjugacy problem (this problem was first proposed by Rips in 1994). The basic concepts and examples will be provided, no specific knowledge will be assumed. Tea at 3:33 pm in Stevenson 1425. (Contact Person: Dechao Zheng)

## Special Colloquium

Location: Stevenson 1206

Tea at 2:30 pm in Stevenson 1425.

## The Rational Homology of the Level 4 Braid Group

Kevin Kordek, Georgia Tech

Location: Stevenson Center 1308

In this talk I will describe recent joint work with Dan Margalit on the rational homology of the level 4 braid group, a finite-index subgroup of the braid group, which is the kernel of the mod 4 reduction of the integral Burau representation. The main results are an explicit description of the first rational homology as a representation of the braid group and a formula for the first Betti number.

## Reﬁned Invariants of Algebraic Knots and Number Theory

Ivan Cherednik,University of North Carolina-Chapel Hill

Location: Stevenson 5211

The (uncolored) HOMFLY-PT polynomials H(q,a), are relatively simple to define for any links. We will consider only algebraic knots: intersections of connected plane curve singularities with small 3-dimensional sphere centered at the singularity. Their t-refinements, the Khovanov-Rozansky stable reduced polynomials KhR(q,t,a) attract a lot of attention. This is the most powerful numerical invariant of knots we have, though difficult to calculate. The connection is H(q,a)=KhR(q,q,-a). This talk will be about the motivic superpolynomials which will be defined from scratch; very little knowledge of rings and modules is needed (and finite fields). Conjecturally, they coincide with stable, reduced Khovanov-Rozansky polynomials. Moreover, and this will be explained in full, they are conjectured to coincide with the L-function of the ring of plane curve singularity over the finite field of cardinality “q” (a two-line definition); “t” becomes simply “T” from the theory of local zeta-functions. The implications of this interplay between knot theory (with almost infinite list of applications) and number theory will take time to digest, but this is obviously of fundamental nature. For instance, the Riemann Hypothesis for t-zeros of the motivic superpolynomials holds for sufficiently small “q” (a theorem); presumably for “q” smaller than 1/2 at a=0. Tea at 3:33 pm in Stevenson 1425. (Contact Person: Larry Rolen)

## Talk Title TBA

Mahdi Mohebbi, SUNY Korea

Location: Stevenson 1307

## DAHA-Invariants of Algebraic Knots

Ivan Cherednik, UNC Chapel Hill

Location: Stevenson 1432

For algebraic links, stable Khovanov-Rozansky polynomials are conjectured to coincide with DAHA superpolynomials. We will define Double Affine Hecke Algebras, DAHA, of sl2-type and construct the refine DAHA-Jones polynomials for torus knots. The case of trefoil will be considered in detail and we will demonstrate the passage from DAHA-Jones polynomials to DAHA superpolynomial for trefoil (which is 1 + qt + aq). Then we will switch to torus iterated knots (including all algebraic knots). The Rosso-Jones formula is missing for the Khovanov-Rozansky polynomials (unless for q = t, which is the reduction to HOMFLY-PT polynomials). Interestingly, some its counterparts exist in the DAHA setting (at least in examples). The key here is actually the theory of the DAHA-Verlinde algebras (related to the WZW and WZWH models), but the DAHA superpolynomials are given directly in terms DAHA. Verlinde algebras are quotients of their polynomial representations at roots of unity, which will be explained. Here a link to subfactors can be expected. The universality of DAHA is actually not surprising: they are deformations of the Heisenberg/Weyl algebras (and generalizations of Hecke algebras). What is surprising is that the same superpolynomials can be conjecturally obtained directly from plane curve singularities without any representation theory; this connection will be stated. It may be related to the passage from the Landau-Ginzburg Sigma Models with superpotentials W (equations of singularities) to Super Conformal Field Theories, say to the Vafa-Warner’s paper “Catastrophes…” (1989). If time permits, I will try to discuss this a bit.

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Dennis Sullivan, Suny at Stony Brook

Location: Stevenson 5211

Tea at 3:33 pm in Stevenson 1425. (Contact Person: Marcelo Disconzi)

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Naian Liao, Chongqing University, China

Location: Stevenson 1307

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Kyle Austin, Weizmann Institute

Location: Stevenson 1308

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Alex Furman, University of Illinois at Chicago

Location: Stevenson 5211

Tea at 3:33 pm in Stevenson 1425. (Contact Person: Spencer Dowdall)

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Ryan Solava, Vanderbilt University

Location: Stevenson 1206

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Irena Lasiecka, University of Memphis

Location: Stevenson 1307

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Zack Tripp, Vanderbilt University

Location: Stevenson 1206

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Arie Levit, Yale University

Location: Stevenson Center 1308

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Kate Ponto, University of Kentucky

Location: Stevenson 1310

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Steven Lalley, University of Chicago

Location: Stevenson 5211

Tea at 3:33 pm in Stevenson 1425. (Contact Person: Mark Sapir)

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Sayan Das, University of Iowa

Location: Stevenson 1432

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Huy Nguyen, Brown University

Location: Stevenson 1307

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Sergei Tabachnikov, Pennsylvania State University

Location: Stevenson 5211

Tea at 3:33 pm in Stevenson 1425. (Contact Person: Mark Sapir)

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Jeremy LeCrone, University of Richmond

Location: Stevenson 1307

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Yuanzhen Shao, Georgia Southern University

Location: Stevenson 1307

## Shanks Workshop on Homotopy Theory 2019, April 13-14

Locations: Stevenson Center 1 (Math Building)

For more information, visit the workshop website.

## Talk Title TBA

Vladimir Sverak, University of Minnesota

Location: Stevenson 5211

Tea at 3:33 pm in Stevenson 1425. (Contact Person: Gieri SImonett)

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Christian Zillinger, University of Southern California

Location: Stevenson 1307

## Spring 2019 Semester

Location: Vanderbilt University

Undergraduate classes end on April 22, 2019. For more information, Visit the Office of the University Registrar online.

## Talk Title TBA

Gerard Misiolek, University of Notre Dame

Location: Stevenson 1307

## NCGOA Spring Institute 2019 and 34th Annual Shanks Lecture, May 3-9

Location: Stevenson Center 4309

The topic of the Seventeenth Annual Spring Institute on Noncommutative Geometry and Operator Algebras is “Algebra and Geometry Quantized and Quantified.” The conference will focus on common themes and recent developments in topology, quantum algebra, topological condensed matter physics, subfactor theory, and quantum information theory. NCGOA 2019 will be held in conjunction with the 34th Shanks Lecture, delivered by Fields Medalist Michael Freedman (Microsoft Research). More information is available on the conference website.

## Approximation Theory 16, May 19-22, 2019

Location: Vanderbilt University

This meeting will be the sixteenth in a series of international conferences on Approximation Theory held every three years at various locations in the U.S. For more information, please visit the conference website.