Events for 02/07/2020 from all calendars

Working Seminar on Quantum Computation and Quantum Information

Time: 2:00PM - 3:00PM

Location: Bloc 624

Speaker: Samuel Harris, TAMU MATH

Title: Superdense Coding and Quantum Teleportation

Seminar on Banach and Metric Space Geometry

Time: 3:00PM - 4:00PM

Location: BLOC220

Speaker: Ilya Razenshteyn, Microsoft Research Redmond

Title: Spectral Partitioning of Metric Spaces

Abstract: I will show how to build efficient nearest neighbor search data structures for general metric spaces using a novel randomized partitioning procedure which is closely related to metric spectral gaps. Based on joint work with Alex Andoni, Assaf Naor, Sasho Nikolov and Erik Waingarten.

Algebra and Combinatorics Seminar

Time: 3:00PM - 3:50PM

Location: BLOC 628

Speaker: Luca Schaffler, University of Massachusetts Amherst

Title: A Pascal's theorem for rational normal curves

Abstract: Pascal's theorem gives a synthetic geometric condition for six points A,...,F in the projective plane to lie on a conic. Namely, that the intersection points of the lines AB and DE, AF and CD, EF and BC are aligned. In higher dimension, one could ask: is there a coordinate-free condition for d+4 points in d-dimensional projective space to lie on a degree d rational normal curve? We find many of these conditions by writing in the Grassmann-Cayley algebra the defining equations of the parameter space of d+4 ordered points that lie on a rational normal curve of degree d. This is joint work with Alessio Caminata.

Geometry Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: Changho Han, University of Georgia

Title: Counting hyperelliptic curves over global fields of bounded height via hyperelliptic fibrations

Abstract: A hyperelliptic curve y^2=f(x) with coefficients in a global field (such as Q) comes equipped with a natural invariant called the height of the discriminant. Then, it is a natural question to find the asymptotic behavior of a function counting the number of reasonably behaving hyperelliptic curves with bounded height B. However, this problem turns out to be wide open if the base field is a number field. By jointly working with Junyong Park, we instead consider this problem for function fields, namely F_q(t) the generic point of a projective line over F_q. In this case, we can reinterpret hyperelliptic curves as hyperelliptic fibrations over P^1, allowing us to use both geometry of algebraic surfaces and arithmetic of the space of maps from P^1 into moduli spaces of hyperelliptic curves. By using this observation, I will illustrate the counting function over F_q(t) (which heuristically expect to look similar to that of number fields) and related results along the way (such as motive/point count of relevant moduli spaces and birational geometry involved).

Linear Analysis Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Wencai Liu, Texas A&M University

Title: The gap labeling conjecture and the dry Ten Martini Problem

Abstract: The "Ten Martini Problem" dubbed after Marc Kac and Barry Simon states that the almost Mathieu operator with irrational flux has Cantor spectrum, which has been solved by Avila and Jitomirskaya completely about 10 years ago. The stronger conjecture (the dry Ten Martini Problem) predicted all spectral gaps with canonical labels are non-collapsed is still open. In this talk, I will present two equivalent formulations of the gap labeling conjecture (K-Theory and dynamical system) and discuss two corresponding approaches to tackle the dry Ten Martini problem. More precisely, I will firstly introduce the method by Choi-Elliot-Yui via writing the almost Mathieu operator as the irrational rotation C*-algebra with two canonical unitary generators. Secondly, I will introduce another approach by Avila, Avila-Jitomirskaya (with the generalization by Yuan and me), Eliasson, Sinai, and others via studying the dynamics of a family of linear skew-products driven by irrational rotation on cocycles.