Sponsored by the UW Department of Mathematics and the Pacific Institute for the Mathematical Sciences.
April 29, 2016 at 2:30pm MEB 248 

Anthony VárillyAlvarado Rice University 
K3 surfaces and cubic fourfolds 
The group E(Q) of points on an elliptic curve over the rational numbers is known to be finitely generated, by work of Mordell. In an astonishing 1977 paper, Barry Mazur proved there are only 15 possibilities for the torsion subgroup of E(Q). I will discuss a conjecture on the arithmetic of K3 surfaces that I will argue is an analogue to Mazur's theorem, despite the absence of a group law on a K3 surface! I will offer some initial evidence for this conjecture, based on joint work with McKinnie, Sawon, and Tanimoto, as well as separate joint work with Tanimoto on moduli of special cubic fourfolds. 

April 22, 2016 at 2:30pm MEB 248 

June Huh Princeton University 
Hard Lefschetz theorem and HodgeRiemann relations for combinatorial geometries 
A conjecture of Read predicts that the coefficients of the chromatic polynomial of a graph form a logconcave sequence for any graph. A related conjecture of Welsh predicts that the number of linearly independent subsets of varying sizes form a logconcave sequence for any configuration of vectors in a vector space. In this talk, I will argue that two main results of Hodge theory, the Hard Lefschetz theorem and the HodgeRiemann relations, continue to hold in a realm that goes beyond that of Kahler geometry. This implies the above mentioned conjectures and their generalization to arbitrary matroids. 

April 1, 2016 at 2:30pm MEB 248 

Katherine E. Stange University of Colorado, Boulder 
A Farey Tour 
I will begin with the familiar Farey sequences: the subdivisions of the real line obtained by recursively taking the mediant (a+c)/(b+d) of fractions a/b and c/d. I will take this starting point as an excuse for an ecclectic tour which may include such topics as continued fractions, topographs, hyperbolic geometry, ergodic theory, and even Apollonian circle packings. In particular, I'd like to generalize these classical connections to the case of Gaussian integers and beyond. 

March 4, 2016 at 2:30pm MEB 248 

Dusa McDuff Barnard College 
Embedding Questions in Symplectic Geometry 
A symplectic structure is a kind of geometric structure that can be put on an even dimensional space. It generalizes the notion of an area form in two dimensions in such a way that many of the special dynamical features of area preserving geometry (such as the existence of extra fixed points) persist. However the global properties of this geometry are still not well understood. This will be a talk for nonspecialists that explains some known facts and some open problems, concentrating on recent progress in understanding symplectic embeddings. 

February 12, 2016 at 2:30pm MEB 248 

Brian Conrad Stanford University 
The ABC Conjecture 
The ABC Conjecture, formulated in the mid1980's by Oesterlé and Masser, is one of the most important conjectures in number theory. It has many deep consequences, but its basic formulation can be given in entirely elementary terms. In September 2012, a 500page solution was announced by Shinichi Mochizuki (building on several thousand pages of work that he has carried out over the last 20 years). I will explain what the conjecture asserts, some evidence that supports it, a few of its consequences, and some of the circumstances surrounding the evaluation of the proof by the number theory community. 

November 20, 2015 at 2:30pm SIG 225 

Jennifer McLoudMann University of Washington, Bothell 
iBlock Transitive Tilings by Convex Pentagons 
This talk will concern tilings of the plane by polygons. A tiling (or tessellation) of the plane is a covering of the plane by shapes (called the tiles of the tiling) in which the interiors of the tiles are disjoint. In particular, in this talk we will discuss monohedral tilings by convex polygons; that is, tilings in which all tiles are congruent to a single convex polygon. Convex ngons admitting tilings of the plane have been classified for all n ≠ 5. We will discuss the history of the search for all convex pentagons that tile the plane and our recent contribution to this longstanding unsolved problem. 

November 13, 2015 at 2:30pm SIG 225 

Sham M. Kakade University of Washington 
Tensor Decomposition Approaches for Learning Mixture Models 
In many applications, we face the challenge of modeling the interactions between multiple observations and hidden causes; such problems range from clustering points in space to document retrieval, where we seek to model the underlying topics, to community detection in social networks. The (unsupervised) learning problem is to accurately estimate the model (e.g. the the underlying clusters, hidden topics, or the hidden communities in a social network) with only samples of the observed variables. In practice, many of these models are fit with local search heuristics. This talk will show how (provably accurate) tensor based approaches provide closed form estimation methods for a wide class of these models. 

October 16, 2015 at 2:30pm SIG 225 

Ivan Corwin Columbia University and the Clay Mathematics Institute 
A Drunk Walk in a Drunk World 
In a simple symmetric random walk on Z a particle jumps left or right with 50% chance independently at each time and space location. What if the jump probabilities are taken to be random themselves (e.g. uniformly distributed between 0% and 100%)? In this talk we will describe the effect of this random environment on a random walk, in particular focusing on a new connection to the KardarParisiZhang universality class and to the theory of quantum integrable systems. No prior knowledge or background will be expected. 

October 2, 2015 at 2:30pm SIG 225 

Amnon Yekutieli Ben Gurion University 
Nonabelian Multiplicative Integration on Surfaces 
Nonabelian multiplicative integration on curves is a classical theory, going back to Volterra in the 19th century. In differential geometry this operation can be interpreted as the holonomy of a connection along a curve. In probability theory this is a continuoustime Markov process. 
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