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Series: Stochastics Seminar

The study of graph-partition problems such as Maxcut, max-bisection and
min-bisection have a long and rich history in combinatorics and theoretical
computer science. A recent line of work studies these problems on sparse random
graphs, via a connection with mean field spin glasses. In this talk, we will look
at this general direction, and derive sharp comparison inequalities between cut-sizes on sparse Erdös-Rényi and random regular graphs.
Based on joint work with Aukosh Jagannath.

Series: Graph Theory Seminar

Let G be a graph containing 5 different vertices a0, a1, a2, b1
and b2. We say that (G, a0, a1, a2, b1, b2) is feasible if G contains
disjoint connected subgraphs G1, G2, such that {a0, a1, a2}⊆V(G1) and
{b1, b2}⊆V(G2). In this talk, we will describe
the structure of G when (G, a0, a1, a2, b1, b2) is infeasible, using
frames and connectors. Joint work with Changong Li, Robin Thomas, and
Xingxing Yu.

Series: School of Mathematics Colloquium

Series: School of Mathematics Colloquium

The study of nonconventional sums $S_{N}=\sum_{n=1}^{N}F(X(n),X(2n),\dots,X(\ell n))$, where $X(n)=g \circ T^n$ for a measure preserving transformation $T$, has a 40 years history after Furstenberg showed that they are related to the ergodic theory proof of Szemeredi's theorem about arithmetic progressions in the sets of integers of positive density. Recently, it turned out that various limit theorems of probabilty theory can be successfully studied for sums $S_{N}$ when $X(n), n=1,2,\dots$ are weakly dependent random variables. I will talk about a more general situation of nonconventional arrays of the form $S_{N}=\sum_{n=1}^{N}F(X(p_{1}n+q_{1}N),X(p_{2}n+q_{2}N),\dots,X(p_{\ell}n+q_{\ell}N))$ and how this is related to an extended version of Szemeredi's theorem. I'll discuss also ergodic and limit theorems for such and more general nonconventional arrays.

Series: Analysis Seminar

We introduce a class of operators on abstract measurable spaces, which unifies variety of operators in Harmonic Analysis. We prove that such operators can be dominated by simple sparse operators. Those domination theorems imply some new estimations for Calderón-Zygmund operators, martingale transforms and Carleson operators.

Wednesday, October 4, 2017 - 13:55 ,
Location: Skiles 006 ,
Libby Taylor ,
Georgia Tech ,
Organizer: Jennifer Hom

Let K be a tame knot in S^3. Then the Alexander polynomial is knot invariant, which consists of a Laurent polynomial arising from the infinite cyclic cover of the knot complement. We will discuss the construction of the Alexander polynomial and, more generally, the Alexander invariant from a Seifert form on the knot. In addition, we will see some connections between the Alexander polynomial and other knot invariants, such as the genus and crossing number.

Series: Research Horizons Seminar

Series: PDE Seminar

The magnetohydrodynamic (MHD) equations govern the motion of electrically conducting fluids such as plasmas, liquid metals, and electrolytes. They consist of a coupled system of the Navier-Stokes equations of fluid dynamics and Maxwell's equations of electromagnetism. Besides their wide physical applicability, the MHD equations are also of great interest in mathematics. They share many similar features with the Navier-Stokes and the Euler equations. In the last few years there have been substantial developments on the global regularity problem concerning the magnetohydrodynamic (MHD) equations, especially when there is only partial or fractional dissipation. The talk presents recent results on the global well-posedness problem for the MHD equations with various partial or fractional dissipation.

Series: Geometry Topology Seminar

I'll introduce you to one of my favorite knotted objects: fibered,
homotopy-ribbon disk-knots. After giving a thorough overview of these
objects, I'll discuss joint work with Kyle Larson that brings some new
techniques to bear on their study. Then, I'll
present new work with Alex Zupan that introduces connections with Dehn
surgery and trisections. I'll finish by presenting a classification
result for fibered, homotopy-ribbon disk-knots bounded by square knots.

Series: Algebra Seminar

A classical theorem in modern homotopy theory states that functors from finite pointed sets to spaces satisfying certain conditions model infinite loop spaces (Segal 1974). This theorem offers a recognition principle for infinite loop spaces. An analogous theorem for Morel-Voevodsky's motivic homotopy theory has been sought for since its inception. In joint work with Marc Hoyois, Adeel Khan, Vladimir Sosnilo and Maria Yakerson, we provide such a theorem. The category of finite pointed sets is replaced by a category where the objects are smooth schemes and the maps are spans whose "left legs" are finite syntomic maps equipped with a K-theoretic trivialization of its contangent complex. I will explain what this means, how it is not so different from finite pointed sets and why it was a natural guess. In particular, I will explain some of the requisite algebraic geometry.Time permitting, I will also provide 1) an explicit model for the motivic sphere spectrum as a torsor over a Hilbert scheme and,2) a model for all motivic Eilenberg-Maclane spaces as simplicial ind-smooth schemes.