Derived categories of cyclic covers and their branch divisors

Alexander Perry
Harvard University
April 29, 2015
Given a variety $Y$ with a rectangular Lefschetz decomposition of its derived category, I will discuss an interesting relation between the derived categories of a cyclic cover of $Y$ and its branch divisor. As examples, I will describe the cases of cyclic cubic fourfolds and "special Gushel--Mukai varieties," where we get a description of the equivariant category of certain K3 categories. This is joint work with Alexander Kuznetsov.

Is the Abstract Mathematics of Topology Applicable to the Real World?

Robert D. MacPherson; Randall D. Kamien; Raúl Rabadán
Hermann Weyl Professor, School of Mathematics; University of Pennsylvania; Columbia University
May 1, 2015
Topology is the only major branch of modern mathematics that wasn't anticipated by the ancient mathematicians. Throughout most of its history, topology has been regarded as strictly abstract mathematics, without applications. However, illustrating Wigner's principle of "the unreasonable effectiveness of mathematics in the natural sciences", topology is now beginning to come up in our understanding of many different real world phenomena.

Reductions of Galois representations of small slopes

Eknath Ghate
Tata Institute of Fundamental Research
May 7, 2015
We investigate the shape of the reduction of certain crystalline Galois representations of integral slope 1 and of fractional slopes in (1,2). The proof uses the compatibility between the p-adic and mod p Local Langlands Correspondences with respect to the process of reduction. We give an essentially complete description of the reduction, and show that in the former case it is generically reducible, whereas in the latter case it is generically irreducible. This is joint work with Shalini Bhattacharya for slopes in (1,2), and also with Sandra Rozensztajn for slope 1.

Bernoulli convolutions for algebraic parameters

Péter Varjú
University of Cambridge
May 8, 2015
The Bernoulli convolution with parameter $\lambda$ is the law of the random variable: $\sum X_i \lambda^i$, where $X_i$ are independent unbiased $+1/-1$ valued random variables. If $\lambda \lambda > 1/2$, the question whether the Bernoulli convolution is singular or a.c. is a very interesting open problem. Recent papers of Hochman and Shmerkin prove that the set of $\lambda$'s such that the measure is singular is of Hausdorff dimension 0. I will discuss the problem for parameters $\lambda$ that are algebraic. Work in progress, joint with Emmanuel Breuillard.

Our Mathematical Universe

Max Tegmark
Professor, Massachusetts Institute of Technology
May 8, 2015
In this lecture, Tegmark surveys how humans have repeatedly underestimated not only the size of the cosmos, but also the power of the human mind to understand it using mathematical equations. He explores how mathematics in physics has allowed us to predict Neptune, radio waves, and the Higgs bosons. Tegmark also discusses how we should think of ourselves in a cosmic perspective.

In Search Of: Failed Supernovae

Christopher Kochanek
Ohio State University
May 12, 2015

Failed supernovae, where core collapse leads to the formation of a black hole without an external supernova, have always been one of the possible outcomes when a massive star dies.  The observed properties of the dying, progenitor stars, mismatches between the star formation and supernova rates, the black hole mass

Tales from the Data Trenches of Display Advertising

Claudia Perlich
Chief Scientist, Dstillery
May 15, 2015
As Chief Scientist at Dstillery, Claudia Perlich works to collect about 10 billion user events daily, representing the digital and geo-physical journeys of millions of people on desktops, tablets, and mobile phones. In this lecture, Perlich will explore a number of challenges including privacy-preserving representations, robust high- dimensional modeling, large-scale automated learning systems, transfer learning, and fraud detection.