# Events for 03/03/2023 from all calendars

## Noncommutative Geometry Seminar

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

**Location: ** ZOOM

**Speaker: **Jinmin Wang , Texas A&M University

**Title: ***Index pairing and quantitative control of scalar curvature*

**Abstract: **In this talk, I will speak about an index theoretical approach to a series of Gromov’s questions related to positive scalar curvature. Our approach is to study the index pairing of the Dirac operator and vector bundles. The concrete construction of index pairing reveals a quantitative control of positive scalar curvature, which results from a new uncertainty principle for Fourier transforms. This is based on joint work with Zhizhang Xie and Guoliang Yu.

## Student/Postdoc Working Geometry Seminar

**Time: ** 1:00PM - 2:30PM

**Location: ** BLOC 628

**Speaker: **Derek Wu, TAMU

**Title: *** New border rank lower bounds for GL(V) invariant tensors II*

## Mathematical Physics and Harmonic Analysis Seminar

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

**Location: ** BLOC 302

**Speaker: **Alejandro Aceves, SMU

**Title: ***On the Fractional nonlinear Schrödinger Equation*

**Abstract: **The concept of the fractional Lapacian as it relates to Levi flights in
comparison to Brownian motion appears in many applications in physics. In this talk we will present our work as it relates to optical physics, in particular in the nonlinear regime where both the discrete and the continuous versions are relevant.

## Algebra and Combinatorics Seminar

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

**Location: ** BLOC 302

**Speaker: **Chun-Hung Liu, Texas A&M University

**Title: ***Proper conflict-free coloring and maximum degree*

**Abstract: **A conflict-free coloring of a hypergraph is a coloring on the vertices such that for every hyperedge, some color appears exactly once on the vertices of this edge. This notion is motivated by a frequency assignment problem of cellular networks and is a generalization of a number of variants of coloring notions of graphs. We prove a general upper bound for the number of colors for (proper) conflict-free coloring involving the maximum degree and rank. It provides improvements about linear coloring and star coloring of graphs with bounded maximum degree and addresses a conjecture of Caro, Petrusevski and Skrekovski on proper conflict-free coloring of graphs. They conjectured that for every d \geq 3, every connected graph with maximum degree at most d has a proper conflict-free coloring with d+1 colors. We prove that (1.655083+o(1))d colors suffice. We also prove that the fractional coloring version of this conjecture is asymptotically true. This is joint work with Daniel Cranston.

## Geometry Seminar

**Time: ** 4:00PM - 4:50PM

**Location: ** BLOC 302

**Speaker: **Yen-Kheng Lim, Xiamen University Malaysia

**Title: ***Solving physics problems from the perspective of (tropical) algebraic geometry*

**Abstract: **I will show how the partition function in statistical mechanics can be interpreted as an algebraic variety. In accordance to earlier literature, the zero-temperature limit is equivalent to taking the tropical limit of the algebraic variety. Previous literature have also generalised the temperature parameter to an *n*-vector. Here, we show that in the case of *n*=2, the two components of this generalised quantity are the inverse temperature and inverse temperature times chemical potential, respectively. Other values of *n* can also be similarly interpreted as various intensive thermodynamic parameters. [Joint work with Mounir Nisse]

## Mathematical Physics and Harmonic Analysis Seminar

**Time: ** 4:00PM - 4:50PM

**Location: ** BLOC 302

**Speaker: **Lim Yen Kheng, Xiamen University Malaysia

**Title: ***Solving physics problems from the perspective of (tropical) algebraic geometry*

**Abstract: **In the first part of the talk, it will be shown how the partition function in statistical mechanics can be interpreted as an algebraic variety. In accordance to earlier literature, the zero-temperature limit is equivalent to taking the tropical limit of the algebraic variety. Previous literature have also generalised the temperature parameter to an n-vector. Here, we show that in the case of n=2, the two components of this generalised quantity are the inverse temperature and inverse temperature times chemical potential, respectively. Other values of n can also be similarly interpreted as various intensive thermodynamic parameters.
The second part of the talk concerns null geodesics in four dimensional spacetimes. In particular, we observe that the condition for null circular orbits defines an A-discriminantal variety. A theorem by Rojas and Rusek for A-discriminants leads to the interpretation that there are two branches of null circular orbits for certain classes of spacetimes. A physical consequence of this theorem is that light rings around generic black holes with non-degenerate horizons are unstable. [Joint work with Mounir Nisse]

## Free Probability and Operators

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

**Location: ** BLOC 306

**Speaker: **Ken Dykema, TAMU

**Title: ***On B-valued circular operators*

**Abstract: **We will briefly introduce B-valued circular operators, where B is a *-algebra. We will describe (and perhaps prove) some results about these, in the special case when B is a commutative C*-algebra and describe how they are relevant to the study of DT-operators.