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# Events for March 7, 2018 from General and Seminar calendars

## Paul Gustafson Thesis Defense: On the Property F Conjecture

**Description:** This thesis solves a question posed by Etingof, Rowell, and Witherspoon: As a modular category, $\Mod-D^\omega(G)$ gives rise to (projective) representations of mapping class groups of compact surfaces with boundary. Are the images of these representations always finite? We answer the above question in the affirmative, generalizing their work in the braid group case. Our approach is to translate the problem into manipulation of colored graphs embedded in the given surface as defined by Kirillov. To do this translation, we use the fact that any such representation associated to a finite group $G$ and 3-cocycle $\omega$ is isomorphic to a Turaev-Viro-Barrett-Westbury (TVBW) representation associated to the spherical fusion category $\text{Vec}_G^\omega$ of twisted $G$-graded vector spaces. As shown by Kirillov, the representation space for this TVBW representation is canonically isomorphic to a vector space spanned by $\text{Vec}_G^\omega$-colored graphs embedded in the surface. By analyzing the action of the Birman generators on a finite spanning set of colored graphs, we find that the mapping class group acts by permutations on a slightly larger finite spanning set. This implies that the representation has finite image.

## Number Theory Seminar

**Abstract:** We give a new definition of higher arithmetic Chow groups for smooth projective varieties defined over a number field, which is similar to Gillet and SoulĂ©'s definition of arithmetic Chow groups. We also give a compact description of the intersection theory of such groups. A consequence of this theory is the definition of a height pairing between two higher algebraic cycles, of complementary dimensions, whose real regulator class is zero. This description agrees with Beilinson's height pairing for the classical arithmetic Chow groups. We also give examples of the higher arithmetic intersection pairing in dimension zero that, assuming a conjecture by Milnor on the independence of the values of the dilogarithm, are non zero. This is a joint work with JosĂ© Ignacio Burgos-Gil from ICMAT, Spain.

## Noncommutative Geometry Seminar

**Abstract:** In this talk, I will discuss Lott's higher eta invariants from a more K-theoretic viewpoint. We not only obtain simpler and conceptual proofs of some of the results in literature, but also give new results regarding rationality of these invariants. The talk is based on joint work with G. Yu.

## AMUSE

**Abstract:** It is often said that Mathematics is the language of Physics. But what does that mean? Indeed, although Physics is ultimately an experimental science, it would be impossible to analyze, describe and understand the results of experiments without the precise and logical framework that Mathematics offers. And it would also not be possible to develop theories and make predictions for as yet unobserved events based on those analyses. We will discuss some simple examples often encountered in Math and Physics courses.

**Time:** 1:00PM - 2:00PM

**Location:** BLOC 624

**Speaker:** Paul Gustafson, Texas A&M University

**Time:** 1:15PM - 2:15PM

**Location:** BLOC 220

**Speaker:** Souvik Goswami, Texas A&M University

**Title:** *Higher arithmetic Chow groups*

**URL:** *Link*

**Time:** 2:00PM - 2:50PM

**Location:** BLOC 628

**Speaker:** Zhizhang Xie, Texas A&M University

**Title:** *Higher eta invariants, Rationality and K-theory of C*-algebras*

**Time:** 6:00PM - 7:00PM

**Location:** BLOC 220

**Speaker:** Dr. Sinjini Sengupta, Texas A&M University, Department of Mathematics

**Title:** *The Intertwining of Mathematics and Physics*