Rohlin's theorem on the signature of Spin 4-manifolds can be restated in terms of the connection between real and complex K-theory given by homotopy fixed points. This comes from a bordism result about Real manifolds versus unoriented manifolds, which in turn, comes from a C2-equivariant story. I'll describe a surprising analogue of this for
larger cyclic 2 groups, showing that the element eta cubed is never detected! In particular, for any bordism theory orienting these generalizations of Real manifolds, the three torus is always a boundary.

Over a field in characteristic zero commutative dgas are well-behaved; otherwise they are not. For instance there isn't a
right-induced model structure on them in the general case. I'll explain some of these issues and advertise symmetric sequences to repair that defect.

Eilenberg-Mac Lane spectra represent singular cohomology and they allow for rather algebraic considerations in stable homotopy theory. Shipley proved that there is a Quillen equivalence between algebras over the Eilenberg-Mac Lane spectrum of the integers, HZ, and differential graded rings. I'll talk about ongoing work with her where we aim at extending her result to commutative HZ-algebras. This builds on a Dold-Kan type theorem for commutative monoids in symmetric sequences.

This talk--aimed for a general audience of neither topologists nor model theorists--will discuss applications of cobordisms to Kontsevich's mirror symmetry conjecture. We'll begin by stating a rough version of the
conjecture, which builds a bridge between symplectic geometry on one hand, and on the other hand, algebraic geometry over the complex numbers. We then discuss how the theory of cobordisms, which studies when two manifolds can be the boundary of another manifold, sheds light on how to generalize the mirror symmetry conjecture, while giving us information about objects in symplectic geometry. (For example, two Lagrangians related by a compact cobordism are equivalent in the Fukaya category.)

Transseries originated some 25 years ago, mainly in Ecalle's work, but also independently in the study of Tarski's problem on the field of reals with exponentiation. Some 20 years ago I formulated some conjectures about the differential field of transseries, and started exploring its model-theoretic properties, first jointly with Matthias Aschenbrenner, and a few years later also in collaboration with Joris van der Hoeven. Around 2011 we finally saw a clear path towards a proof, sharpening the conjectures in the meantime. In the last few weeks we finished the job, with one proviso: as part of a division of labor and for lack of time, some final details have only been checked by some of us, but not yet by all three of us. In any case, I will motivate these conjectures, and give an account of their status.

The talk will be built around  examples of how model theory informs our understanding in areas of mathematics such as algebra, number theory, algebraic geometry and analysis. The model theory behind these applications includes concepts such as compactness, definability, stability and o-minimality. However, we assume  no special expertise in model theory, but rather aim  to illustrate the kinds  of  mathematical questions for which a model theoretical perspective has proven to be useful.

3:45pm
Speaker: Zvi Rosen (UC Berkeley)
Title:   Computing Algebraic Matroids

Abstract: Algebraic matroids characterize the combinatorial structure of an algebraic variety. By decorating the matroid with circuit polynomials and base degrees, we capture even more information about the variety and its coordinate projections.  In this talk, we will introduce algebraic matroids, discuss algorithms for their computation, and present some motivating examples.

5:00pm
Speaker: Noah Giansiracusa (UC Berkeley)
Title:  Equations of Tropical Varieties

Abstract: I'll discuss joint work with J.H. Giansiracusa (Swansea) in which we study scheme theory over the tropical semiring T, using the notion of semiring schemes provided by Toen-Vaquie, Durov, or Lorscheid. We define tropical hypersurfaces in this setting and a tropicalization functor that sends closed subschemes of a toric variety over a field with non-archimedean valuation to closed subschemes of the corresponding toric variety over T. Upon passing to the set of \mathbb{T}-valued points this yields Kajiwara-Payne's extended tropicalization functor. We prove that the Hilbert polynomial of any projective subscheme is preserved by our tropicalization functor, so the scheme-theoretic foundations developed here reveal a hidden flatness in the degeneration sending a variety to its tropical skeleton.