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November 14, 2017


Tuesday, November 14, 2017

Han-Bom Moon "Birational geometry of moduli space of parabolic bundles."
1:00 PM - 2:30 PM


Speaker: Han-Bom Moon, The Institute for Advanced Study Abstract: I will describe a project on birational geometry of the moduli space of parabolic bundles on the projective line in the framework of Mori’s program, and its connection with classical invariant theory and conformal blocks. This is joint work with Sang-Bum Yoo.
Biostatistics Help: Faculty, Staff, Pre and Post Doc Walk-In Clinic
1:30 PM - 2:30 PM

Biostatistics consulting is available to all Johns Hopkins University faculty, staff, pre and post docs conducting clinical and translational research. 1:30 – 2:30 PM Wolfe Street Building Room: E3144
Xuhua He " Some results on affine Deligne-Lusztig varieties"
3:00 PM - 4:30 PM


Speaker: Xuhua He (Maryland) Abstract: In Linear Algebra 101, we encounter two important features of the group of invertible matrices: Gauss elimination method, or the LU decomposition of almost all matrices, which is an important special case of the Bruhat decomposition; the Jordan normal form, which gives a classification of the conjugacy classes of invertible matrices. The study of the interaction between the Bruhat decomposition and the conjugation action is an important and very active area. In this talk, we focus on the affine Deligne-Lusztig variety, which describes the interaction between the Bruhat decomposition and the Frobenius-twisted conjugation action of loop groups. The affine Deligne-Lusztig variety was introduced by Rapoport around 20 years ago and it has found many applications in arithmetic geometry and number theory. In this talk, we will discuss some recent progress on the study of affine Deligne-Lusztig varieties, and some applications to Shimura varieties.
Todd Oluyink "Dynamical relativistic liquid bodies"
4:00 PM - 5:00 PM


Speaker: Todd Oluyink, Monash University Abstract: In this talk, I will discuss a new approach to establishing the well-posedness of the relativistic Euler equations for liquid bodies in vacuum. The approach is based on a wave formulation of the relativistic Euler equations that consists of a system of non-linear wave equations in divergence form together with a combination of acoustic and Dirichlet boundary conditions. The equations and boundary conditions of the wave formulation differs from the standard one by terms proportional to certain constraints, and one of the main technical problems to overcome is to show that these constraints propagate, which is necessary to ensure that solutions of the wave formulation determine solutions to the Euler equations with vacuum boundary conditions. During the talk, I will describe the derivation of the wave equation and boundary conditions, the origin of the constraints, and how one shows that the constraints propagate. Time permitting, I will also discuss how energy estimates can be obtained from this new formulation paying particular attention to the role of the acoustic boundary conditions. Cheers,
Wei Zhang "Archimedes' cattle, Sylvester numbers and Heegner points."
4:30 PM - 5:30 PM


Speaker:Wei Zhang, Abstract:In the first lecture we will discuss two classical Diophantine questions. (1) (Archimedes' cattle problem) what is the smallest (non-trivial) integer solution to the equation x^2 - 410286423278424 y^2 = 1 (2) (Sylvester) what integers can be represented as a sum of two cubes (of rational numbers)? and how their solutions connect to class field theory for the rational number fields, resp., for imaginary quadratic fields.

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