Automorphisms of smooth canonically polarised surfaces in characteristic 2

Nikolaos Tziolas
University of Cyprus
February 25, 2015
Let $X$ be a smooth canonically polarised surface defined over an algebraically closed field of characteristic 2. In this talk I will present some results about the geometry of $X$ in the case when the automorphism scheme $\mathrm{Aut}(X)$ of $X$ is not smooth, or equivalently $X$ has nontrivial global vector fields.

Albert O. Hirschman Prize Ceremony & Lectures

Esther Duflo
Massachusetts Institute of Technology
February 25, 2015
Honoring the 2014 SSRC’s Albert O. Hirschman Prize Recipients

Abhijit Banerjee and Esther Duflo
Co-Directors, Abdul Latif Jameel Poverty Action Lab
Massachusetts Institute of Technology

This program features a talk by Esther Duflo, as well as a panel discussion on her contributions with Margaret Levi (Stanford University) and Christopher Udry (Yale University). This event is co-organized by the School of Social Science and the Social Science Research Council.

Disc filling and connected sum

Kai Zehmisch
Universität Münster
February 27, 2015
In my talk I will report on recent work with Hansjörg Geiges about a strong connection between the topology of a contact manifold and the existence of contractible periodic Reeb orbits. Namely, if the contact manifold appears as non-trivial contact connected sum and has non-trivial fundamental group or torsion-free homology, then the existence is ensured. This generalizes a result of Helmut Hofer in dimension three.

Effective-resistance-reducing flows, spectrally thin trees and asymmetric TSP

Shayan Oveis Gharan
University of California, Berkeley
March 2, 2015
Given a $k$-edge-connected graph $G = (V,E)$, a spanning tree $T$ is $\alpha$-thin w.r.t. $G$, if for any $S \subset V$, $|T(S,V - S)| \leq \alpha.|E(S,V - S)|$. The thin tree conjecture asserts that for a sufficiently large $k$ (independent of size of $G$) every $k$-edge-connected graph has a $1/2$-thin tree. This conjecture is intimately related to designing approximation algorithms for Asymmetric Traveling Salesman Problem (ATSP). We show that any $k$-edge-connected graph has a $\mathrm{polyloglog}(n)/k$-thin spanning tree.

Joint equidistribution of arithmetic orbits, joinings, and rigidity of higher rank diagonalizable actions I

Elon Lindenstrauss
Hebrew University of Jerusalem
March 2, 2015
An important theme in homogenous dynamics is that two parameter diagonalizable actions have much more rigidity than one parameter actions. One manifestation of this rigidity is rigidity of joinings of such actions. Joinings are an important concept in the study of dynamical systems, and allow detection of "hidden common denominator" of two (or more) dynamical systems. While one parameter diagonalizable actions on homogenous spaces have lots of joinings, for two parameter actions any measurable joining can be provided to be in fact of a very precise algebraic kind.

Whitney numbers via measure concentration in representation varieties

Karim Adiprasito
Member, School of Mathematics
March 3, 2015
We provide a simple proof of the Rota--Heron--Welsh conjecture for matroids realizable as c-arrangements in the sense of Goresky--MacPherson: we prove that the coefficients of the characteristic polynomial of the associated matroids form log-concave sequences, proving the conjecture for a family of matroids out of reach for all previous methods. To this end, we study the Lévy--Milman measure concentration phenomenon on natural pushforwards of uniform measures on the Grassmannian to realization spaces of arrangements under a certain extension procedure on matroids.

On some questions about minimal log discrepancies

Mircea Mustata
University of Michigan
March 3, 2015
The minimal log discrepancy is a measure of singularities of pairs. While akin to the log canonical threshold, it turns out to be much more difficult to study, with many questions still open. I will discuss a question about the boundedness of divisors that compute the minimal log discrepancy on a fixed germ. This is joint work (in progress) with Yusuke Nakamura.

On some questions about minimal log discrepancies

Mircea Mustata
University of Michigan
March 3, 2015
The minimal log discrepancy is a measure of singularities of pairs. While akin to the log canonical threshold, it turns out to be much more difficult to study, with many questions still open. I will discuss a question about the boundedness of divisors that compute the minimal log discrepancy on a fixed germ. This is joint work (in progress) with Yusuke Nakamura.

Measuring and Modelling Redshift-space Distortions in the Galaxy Distribution

John Peacock
University of Edinburgh
March 3, 2015

Deviations from a uniformly expanding universe are of interest in modern cosmology, most particularly because the amplitude of such peculiar motions measures the strength of gravity on scales of roughly 10-100 Mpc. I will review various recent attempts to measure these velocity effects in leading galaxy surveys, together with new rapid approximate means of generating the simulated universes that are needed in order to extract validated results from the data.

The jumping coefficients of non-Q-Gorenstein multiplier ideals

Patrick Graf
Universität Bayreuth
March 4, 2015
De Fernex and Hacon associated a multiplier ideal sheaf to a pair $(X, \mathfrak a^c)$ consisting of a normal variety and a closed subscheme, which generalizes the usual notion where the canonical divisor $K_X$ is assumed to be Q-Cartier. I will discuss a recent work of mine on the jumping numbers associated to these multiplier ideals. The set of jumping numbers of a pair is unbounded, countable and satisfies a certain periodicity property.