Events for 02/15/2023 from all calendars

Noncommutative Geometry Seminar

Time: 2:00PM - 3:00PM

Location: BLOC 302

Speaker: Bo Zhu, TAMU

Title: Metric structure of Riemannian manifolds involving their curvature

Abstract: In this talk, we will first introduce some basic concepts(size of Riemannian manifolds) and discuss their relationships with other metric structure quantities. Then, we will introduce some conjectures in this field, which are introduced by Gromov and Yau. Finally, we will present our progress on the estimate of the Uryson 1-width for Riemannian manifolds with uniformly positive mean curvature.

Topology Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Ningchuan Zhang, University of Pennsylvania

Title: Profinite Picard groups in K(n)-local homotopy theory

Abstract: The study of Picard groups in homotopy theory was initiated by Hopkins-Mahowald-Sadofsky. They gave a general framework to compute Picard groups of the categories of $K(n)$-local spectra. In the past decade, significant progress has been made in our understandings of Picard groups with new tools from higher category theory and equivariant homotopy theory. In this talk, we first review the basics of Picard groups in homotopy theory. Then we establish a descent spectral sequence to compute Picard groups of Galois extensions of the $K(n)$-local sphere. One key point in the proof is the profinite topology on the Picard group of a $K(n)$-local $E_\infty$ ring spectra. As an application, we compute Picard groups of all Galois extensions of the $K(1)$-local spheres at all primes. This is joint work in progress with Guchuan Li.

Groups and Dynamics Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: Yury Kudryashov, Texas A&M University

Title: 4-periodic orbits in planar billiards

Abstract: Let Ω be a domain in a Euclidean space of dimension d≥2 with sufficiently smooth boundary. Consider the corresponding billiard: a particle moves along straight lines inside Ω and reflects against the boundary of Ω by the standard reflection law. In 1978, Victor Ivrii conjectured that almost every trajectory of this billiard is non-periodic. This condition appeared as a natural geometric assumption in his theorem about asymptotic behavior of the spectrum of the Dirichlet problem for the Laplace operator in Ω. When this conjecture was formulated, people from Sinai's seminar in Moscow predicted it to be solve in a couple of weeks. More than 40 years later, the conjecture still stands.

Faculty Meeting

Time: 4:00PM - 5:00PM

Location: Bloc 117

AMUSE

Time: 6:00PM - 7:00PM

Location: BLOC 306

Speaker: Kyle Thicke, Texas A&M University

Title: Why simulating quantum physics on a computer is hard (and why quantum computers are awesome)

Abstract: Despite how it sounds, simulating a single quantum particle on a computer is actually quite easy. However, simulating several quantum particles turns out to be an incredibly hard problem. But why? After introducing some quantum mechanics (no prior knowledge required), I will simulate a hydrogen atom with a few lines of code. We will then look into why it is so much more difficult to simulate, e.g., 10 particles. Rather than being 10 times as hard, it turns out to be more like 10,000,000,000 times as hard! As an added bonus, we will show that the reason simulating quantum particles is hard is precisely the reason why quantum computers will be powerful. We will see how a quantum algorithm can easily solve a difficult problem by essentially trying all possibilities at once.