Mathematics | Michigan State University

Department of Mathematics

Seminars By Semester

Seminar: Semester:

Show past talks?

Download iCal

Talk_id	Date	Speaker	Title
13343	Tuesday 5/22 1:00 PM		From Picard groups of hyperelliptic curves to class groups of quadratic fields New Window Algebra Title: From Picard groups of hyperelliptic curves to class groups of quadratic fields Date: 05/22/2018 Time: 1:00 PM - 2:00 PM Place: C304 Wells Hall Speaker: Let C be a hyperelliptic curve defined over Q, whose Weierstrass points are defined over extensions of Q of degree at most three, and at least one of them is rational. Generalizing a result of R. Soleng (in the case of elliptic curves), we prove that any line bundle of degree 0 on C which is not torsion can be specialized into ideal classes of imaginary quadratic fields whose order can be made arbitrarily large. This gives a positive answer, for such curves, to a question by Agboola and Pappas.
13344	Monday 6/11 4:10 PM	Xinliang An, University of Toronto / National University of Singapore	How to Make a Black Hole New Window Analysis and PDE Title: How to Make a Black Hole Date: 06/11/2018 Time: 4:10 PM - 5:00 PM Place: C304 Wells Hall Speaker: Xinliang An, University of Toronto / National University of Singapore Black holes are predicted by Einstein's theory of general relativity, and now we have ample observational evidence for their existence. However theoretically there are many unanswered questions about how black holes come into being. In this talk, with tools from hyperbolic PDE, quasilinear elliptic equations, geometric analysis and dynamical systems, we will prove that, through a nonlinear focusing effect, initially low-amplitude and diffused gravitational waves can give birth to a black hole region in our universe. This result extends the 1965 Penrose’s singularity theorem and it also proves a conjecture of Ashtekar on black-hole thermodynamics. Open problems and new directions will also be discussed.

Contact

Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824
Phone: (517) 353-0844
Fax: (517) 432-1562

College of Natural Science

HOME