Spring 2018

** Organizers: Anna Marie Bohmann, Ioana Suvaina, ****Rares
Rasdeaconu**

** Fridays,
3:10-4:00pm in SC 1310 (unless otherwise noted) **

However, even when the complexes are spheres, low dimensional calculations appear noisy and random. The key to developing a

structure was to find large-scale periodic phenomena, a point of view initiated by Adams in the 1960s using K-theory. Forty years

later we have gotten very good at this, especially after work of Hopkins and his coauthors connecting this study to arithmetic geometry,

including the geometry of elliptic curves. In this talk, I hope to offer a window into this world, and explain some of the beautiful

patterns and symmetries we have found.

Friday, March 2 - no meeting

number of degrees of freedom of the system. This technique is nowadays known as symplectic reduction. Guillemin and Sternberg

considered the problem: what is the quantum analogue of symplectic reduction? In other words, when one quantizes both a mechanical

system with symmetries and its reduced system, what is the relationship between the two quantum-mechanical systems that one obtains?

This is the so-called quantization commutes with reduction theorem. I will give an introduction to this theorem and then talk about its

various generalization and its application in index theory. (Contact Person: Rudy Rodsphon)

Friday, March 23rd

sketch applications for this extension --- for example, the rank filtration in algebraic K-theory due to Quillen seems closely related with

the classical scissors congruence group. (Contact Person: Anna Marie Bohmann)

Friday, March 30th

Quillen in the 70s showed that these invariants fundamentally come from topology: they are a sequence of abelian groups arising as the higher

homotopy groups of a space. There are now a wide range of methods for building this space from an input category, each having different

advantages. In particular, many of these methods are "multiplicative," in that when the starting category has a sort of multiplication, the homotopy

groups of the space produced form a graded ring. In this talk, I will discuss what this means and why we care, and then discuss some recent work

with Osorno in which we compare the multiplication structures produced by two different methods.

long geodesic segment, when properly scaled, looks locally like a Poisson line process. This implies that the global statistics of the tessellation --

for instance, the fraction of triangles -- approach those of the limiting Poisson line process. (Contact Person: Spencer Dowdall)

April 14-15,

of the choice of a hypersurface, and by this reason provides, as a consequence, a strong lower bound on the honest count. In this invariant signed count

the input of a line is given by its local contribution to the Euler number of a certain auxiliary universal vector bundle.

The aim of the talk is to present other, in a sense more geometric, interpretations of the signs involved in the invariant count. In particular, this provides

certain generalizations of Segre indices of real lines on cubic surfaces and Welschinger weights of real lines on quintic threefolds.

This is a joint work with S.Finashin. (Contact Person: Rares Rasdeaconu)