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# Events for 02/17/2020 from all calendars

## Geometry Seminar

## Student Working Seminar in Groups and Dynamics

## Working Seminar on Quantum Computation and Quantum Information

## Students Working Seminar in Number Theory

## Spectral Theory Reading Seminar

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

**Location:** BLOC 628

**Speaker:** Da Rong Cheng, University of Chicago

**Title:** *Bubble tree convergence of cross product preserving maps*

**Abstract:** We study a class of weakly conformal 3-harmonic maps, called Smith maps, which parametrize associative 3-folds in 7-manifolds equipped with G2-structures. These maps satisfy a first-order system of PDEs generalizing the Cauchy-Riemann equation for J-holomorphic curves, and we are interested in their bubbling phenomena. Specifically, we first prove an epsilon-regularity theorem for Smith maps in W^{1, 3}, and then explain how that combines with conformal invariance to yield bubble trees of Smith maps from sequences of such maps with uniformly bounded 3-energy. When the G2-structure is closed, we show that both 3-energy and homotopy are preserved in the bubble tree limit. The result can be viewed as an associative analogue of the bubble tree convergence theorem for J-holomorphic curves. This is joint work with Spiro Karigiannis and Jesse Madnick.

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

**Location:** BLOC 111

**Speaker:** Arman Darbinyan

**Title:** *Lacunary hyperbolicity and algorithmic problems in groups*

**Abstract:** Lacunary hyperbolicity was introduced by Osin, Olshanskii and Sapir as a natural generalization of hyperbolicity from the class of finitely presented groups to the class of finitely generated groups. I will discuss the concept of lacunary hyperbolicity and opulent behavior of classical group theoretical algorithmic problems in that class.

**Time:** 3:30PM - 4:30PM

**Location:** BLOC 506A

**Speaker:** Kari Eifler, TAMU MATH

**Title:** *Introduction to Topological Quantum Computation*

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

**Location:** Bloc605ax

**Speaker:** Erik Davis, Texas A&M University

**Title:** *An Elementary Proof of Bertrand's Postulate*

**Abstract:** In 1845, Bertrand conjectured that for every natural number n beyond 1, there exists a prime between n and 2n. Bertrand was not able to prove this conjecture but had verified the truth of the statement for each n up to 3,000,000. In 1850, Chebyshev proved the result using techniques of complex analysis and a shorter analytic proof was later given by Ramanujan. Despite the simple statement of the theorem, the mathematical community was not successful in finding an elementary proof of the result until 1932, when an 18 year old Paul Erdős deduced the result by observing a few properties of the central binomial. In this talk, I will provide the elementary proof first given by Paul Erdős.

**Time:** 4:10PM - 5:00PM

**Location:** BLOC 624

**Speaker:** Petr Naryshkin, Texas A&M University

**Title:** *Floquet Theory II*

**Abstract:** I will present Chapter II of " The Spectral Theory of Periodic Differential Equations" by M. S. P. Eastham.

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