This course provides the opportunity to offer a new topic in the subject of mathematics.

Seminars

Agnes Beaudry (UChicago) - The Chromatic Splitting Conjecture at $n=p=2$

Understanding the homotopy groups of the sphere spectrum $S$ is one of the great challenges of homotopy theory. The ring $\pi_*S$ is extremely complex; there is no hope of computing it completely. However, it carries an amazing amount of structure. A famous theorem of Hopkins and Ravenel states that, after localizing at a prime, the sphere spectrum is filtered by ``simpler" spectra called the chromatic layers, which we denote by $L_nS$. How these layers interact with each other is a mystery. A conjecture of Hopkins, the chromatic splitting conjecture, suggests an answer to the problem. The difficulty of the problem grows fast with $n$, and varies with the choice of prime at which we localize. The chromatic splitting conjecture is known to hold in its strongest form at all primes $p$ when $n=1$, and at all odd primes when $n=2$. However, it does not hold when $p=n=2$. In this talk, I explain why it fails in this case.

" class="addtocalendar" target="_new">Add to Google CalendarVadim Gorin (MIT) - Integrable two-dimensional stochastic systems and their asymptotic behavior

http://www.mccme.ru/~vadicgor/

I will speak about a class of probabilistic systems that can be analyzed by essentially algebraic methods. The class includes stepped surfaces, six-vertex model ("square ice"), spectra of random matrices, TASEP-like interacting particle systems, directed polymers in random media, etc. We will discuss the asymptotic behavior of these systems, which is governed by universal limiting objects such as the Gaussian Free Field and Tracy-Widom distributions.

" class="addtocalendar" target="_new">Add to Google CalendarTBA - TBA

Tea Time

Andrew Linshaw (Denver) - T-duality and the chiral de Rham complex

http://web.cs.du.edu/~alinshaw/

T-dual pairs are distinct manifolds equipped with closed 3-forms that admit isomorphism of a number of classical structures including twisted de Rham cohomology, twisted K-theory, and twisted Courant algebroids. An ongoing program is to study T-duality from a loop space perspective; that is, to identify structures attached to the loop spaces that are isomorphic under T-duality. In this talk, I'll explain how the chiral de Rham complex of Malikov, Schechtman, and Vaintrob, gives rise to such structures. This is a joint work with Varghese Mathai (University of Adelaide).

Add to Google CalendarNathan Glatt-Holtz (Virginia Tech) - Stochastic PDEs and Turbulence

http://www.math.vt.edu/people/negh/

I will survey some recent results concerning the ergodic theory of nonlinear stochastic PDEs and describe how these results have bearing on various statistical theories of turbulent fluid flow.

Add to Google CalendarMichael Andrews - Non-nilpotent elements in motivic homotopy theory

Classically, the nilpotence theorem of Devinatz, Hopkins, and Smith tells us that non-nilpotent self maps on finite p-local spectra induce nonzero homomorphisms on BP-homology. Motivically, over C, this theorem fails to hold: we have a motivic analog of BP and while $\eta:S^{1,1,}\to S^{0,0}$ induces zero on BP-homology, it is non-nilpotent. Work with Haynes Miller has led to a calculation of $\eta^{-1}\pi_{*,*}(S^{0,0})$, proving a conjecture of Guillou and Isaksen.

I’ll introduce the motivic homotopy category and the motivic Adams-Novikov spectral sequence before describing this theorem. Then I’ll show that there are more periodicity operators in chromatic motivic homotopy theory than in the classical story. In particular, I will describe a new non-nilpotent self map.

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MATH 6559

This course provides the opportunity to offer a new topic in the subject of mathematics.