Tuesday January 22 at 12:00 PM to 1:00 PM in SAS 4201
Diversity and Inclusion in Mathematical and Statistical Sciences
Brown Bag Lunch

Tuesday January 22 at 2:30 PM to 3:00 PM in SAS 4104
Departmental Event
Departmental Tea and Cookies

Wednesday January 23 at 3:00 PM to 4:00 PM in SAS 4201
Special Seminar
Brian Collier, University of Maryland, Higher Teichmüller spaces and Higgs bundles
The Teichmüller space of a surface is a rich mathematical object which can be interpreted from many different perspectives. For example, Teichmüller space can be thought of as a moduli space of hyperbolic structures, Riemann surface structures, or representations of the fundamental group into PSL(2,R) which are discrete and faithful. The aim of higher Teichmüller theory is to identify components of the moduli space of representations of the fundamental group into higher rank Lie groups which generalize discrete and faithful representations. Once identified, one then tries to generalize the different geometric perspectives of Teichmüller space. In this talk, I will discuss recent work identifying new (and conjecturally all) higher Teichmüller components and a generalization of the uniformization theorem known as Labourie's conjecture. To study these problems we transfer the question to a moduli space of holomorphic objects on a Riemann surface called Higgs bundles. At first glance, Higgs bundles are more complicated objects than representations, however, the complicated nature of the objects translates into a rich moduli space equipped with many powerful tools to study it.
Dr. Brian Collier is currently a NSF Postdoctoral Fellow at University of Maryland. He received his Ph.D. from University of Illinois (UIUC) in 2016. Dr. Collier is being interviewed for a tenuretrack Assistant Professor position in the Mathematics Department.

Friday January 25 at 3:00 PM to 4:00 PM in SAS 2102
Graduate Training Seminar
Joint Math Meetings Roundup, Panel of Graduate Students

Friday January 25 at 3:00 PM to 4:00 PM in SAS 4201
Special Seminar
Teng Fei, Columbia University, The HullStrominger system over Riemann surfaces
The HullStrominger system is a system of nonlinear PDEs describing the geometry of compactification of heterotic strings with flux to 4d Minkowski spacetime, which can be regarded as a generalization of Ricciflat Kahler metrics coupled with Hermitian YangMills equation on nonKahler CalabiYau 3folds. In this talk, we present an explicit construction of smooth solutions to the HullStrominger system with infinitely many topological types and sets of Hodge numbers, thus showing that there may be infinitely many candidates in the string theory landscape when flux is present.
Dr. Teng Fei is currently a Ritt Assistant Professor at Columbia University. He received his Ph.D. from MIT in 2016. Dr. Fei is being interviewed for a tenuretrack Assistant Professor position in the Mathematics Department.




