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# Events for April 16, 2018 from General and Seminar calendars

## Mathematical Physics and Harmonic Analysis Seminar

**Abstract:** Chebyshev polynomials for a compact subset e ⊂ R are defined to be the monic polynomials with minimal $||·||_∞ $ over e. In 1969, Widom made a conjecture about the asymptotics of these polynomials when e was a finite gap set. We prove this conjecture and extend it also to those infinite gap sets which obey a Parreau–Widom and a Direct Cauchy Theory condition. This talk will begin with a generalities about Chebyshev Polynomials. This is joint work with Jacob Christiansen and Maxim Zinchenko and partly with Peter Yuditskii.

## Geometry Seminar

**Abstract:** In this talk, we will discuss the stability behavior of the U_q(sl(2))-colored Jones polynomial, a quantum link invariant that assigns to a link K in S^3 a sequence of Laurent polynomials {J_K^n(q)} from n=2 to infinity. The colored Jones polynomial is said to have a tail if there is a power series whose coefficients encode the asymptotic behavior of the coefficients of J_K^n(q) for large n. Since Armond and Garoufalidis-Le proved the existence of a tail for the colored Jones polynomial of an adequate knot, first conjectured by Dasbach-Lin, it has been conjectured that multiple tails exist for all knots. Moreover, the stable coefficients of the tail have been shown to relate to the topology and the geometry of the alternating link complement, prompting the Coarse Volume Conjecture by Futer-Kalfagianni-Purcell. I will talk about an unexpected example of a knot, recently discovered in joint work with Roland van der Veen, where the colored Jones polynomial does not admit a tail, and discuss potential ways to view this example in the context of the categorification of the polynomial, the aforementioned Coarse Volume Conjecture, and a general conjecture made by Garoufalidis-Vuong concerning the stability of the colored Jones polynomial colored by irreducible representations of Lie algebras different from U_q(sl(2)).

## Working Seminar in Groups, Dynamics, and Operator Algebras

## Mathematical Physics and Harmonic Analysis Seminar

**Abstract:** This is not a mathematics talk but it is a talk for mathematicians. Too often, we think of historical mathematicians as only names assigned to theorems. With vignettes and anecdotes, I'll convince you they were also human beings and that, as the Chinese say, "May you live in interesting times" really is a curse.

## Industrial and Applied Math

**Time:** 1:50PM - 2:50PM

**Location:** BLOC 220

**Speaker:** Barry Simon , Caltech

**Title:** *Szegő–Widom asymptotics for Chebyshev polynomials on subsets of R*

**Time:** 3:00PM - 4:00PM

**Location:** BLOC 628

**Speaker:** Christine Lee, UT Austin

**Title:** *A knot with no tail*

**Time:** 3:00PM - 3:50PM

**Location:** BLOC 506A

**Speaker:** Xin Ma, Texas A&M University

**Title:** *Paradoxical comparison and pure infiniteness of crossed products*

**Time:** 4:00PM - 5:00PM

**Location:** BLOC 117

**Speaker:** Barry Simon , Caltech

**Title:** *A colloquium talk: Tales of our Forefathers*

**Time:** 4:00PM - 5:00PM

**Location:** BLOC 117

**Speaker:** Barry Simon, California Institute of Technology

**Title:** *TBA*