Mathematics Colloquium

The Mathematics Department Colloquium is a quarterly series of invited speakers from all mathematical fields and geared toward a broad audience. Archives can be found here

The talks are generally every Tuesday from 4-5 PM, with an informal tea beforehand. For the duration of COVID-19, it will be held via Zoom, with a meet-and-greet 30m before the talk-- bring your own beverage.

Winter 2021 Math Colloquium
*** dates and times as given below ***
"tea" (meet-and-greet) @ ~30m before the talk
Meeting ID: 276-046-2984, Passcode: 962595. [Direct link]
For further information please contact
Professor Francois Monard or call 831-459-1525

Schedule (click dates for title and abstract) 

Tues 1/19 @ 4pm PST Emily Clader SF State University
Thurs 1/21 @ 9am PST Tam Nguyen Phan Institute of Algebra and Geometry; Karlsruhe Institute of Technology
Fri 1/22 @ 2pm PST Nick Salter Columbia University
Tues 2/2
Thur 2/4
Tues 2/9
Thur 2/11
Tues 2/16
Thur 2/18
Tues 2/23 hold for other event
Tues 3/2
Tues 3/9 @ 4pm PST Alexandra Kjuchkova U Penn

Tuesday, January 19, at 4pm

Emily Clader, SF State University

Permutohedral Complexes and Curves With Cyclic Action

There is a beautiful combinatorial story connecting a polytope known as the permutohedron, the algebra of the symmetric group, and the geometry of a particular moduli space of curves first studied by Losev and Manin. I will describe these three seemingly disparate worlds and their connection to one another, and then I will discuss joint work with C. Damiolini, D. Huang, S. Li, and R. Ramadas that generalizes the story to a family of "permutohedral complexes", a family of complex reflection groups, and a new family of moduli spaces.

Thursday, January 21, at 9am

Tam Nguyen Phan, Institute of Algebra and Geometry; Karlsruhe Institute of Technology

Flat cycles in the homology of congruence covers of SL(n,)\SL(n,)/SO(n)

The locally symmetric space SL(n,)\SL(n,)/SO(n), or the space of flat n-tori of unit volume, has immersed, totally geodesic, flat tori of dimension (n − 1). These tori are natural candidates for nontrivial homology cycles of manifold covers of SL(n,)\SL(n,)/SO(n). In joint work with Grigori Avramidi, we show that some of these tori give nontrivial rational homology cycles in congruence covers of SL(n,)\SL(n,)/SO(n). We also show that the dimension of the subspace of the (n − 1)-homology group spanned by flat (n − 1)-tori grows as one goes up in congruence covers. The prerequisite for this talk is very basic linear algebra.

Friday, January 22, 2021

Nick Salter, Columbia University

Families of Riemann surfaces and higher spin structures

Riemann surfaces are central objects in mathematics, bringing complex analysis, algebraic geometry, topology, group theory, dynamics (and more) into close conversation. In many situations, Riemann surfaces occur in families that parameterize some additional algebraic or geometric structure that can be placed on a fixed underlying topological surface. The first part of this talk will be an introduction to families of Riemann surfaces, with an emphasis on the topological aspects of the theory. In the second part, I will discuss some of my own contributions (in collaboration with Aaron Calderon and Pablo Portilla Cuadrado), concerning families of Riemann surfaces equipped with so-called higher spin structures, which arise in a surprising diversity of settings (linear systems on algebraic surfaces, singularity theory, Teichmüller dynamics).

Tuesday, March 9, 2021

Alexandra Kjuchkova, U of Pennsylvania