Artists Present: Michele Beck

Michele Beck
New School University
April 8, 2015
Michele Beck has received acclaim for her work in video and performance. In her videos she often films herself wearing costumes of her own making, concealing her entire body, head and face. In My Erotic Body, a work that could broadly be characterized as documentary, she turns her attention to the recent trends in pole dancing. An act that we associate with strip clubs and various forms of misogyny, pole dancing has been reinvented as a women-only activity, which brings together movement and eroticism in an environment totally isolated from men.

The André-Oort conjecture follows from the Colmez conjecture

Jacob Tsimerman
University of Toronto
April 9, 2015
The André-Oort conjecture says that any subvariety of a Shimura variety with a Zariski dense set of CM points must itself be a Shimura subvariety. In recent years, this has been the subject of much work. We explain how this conjecture for the moduli space of principally polarized abelian varieties of some dimension $g$ follows from current knowledge and a conjecture of Colmez regarding the Faltings heights of CM abelian varieties--in fact its enough to assume an averaged version of the Colmez conjecture.

Restoration as Event and Idea: Art in Europe, 1814‒1820

Thomas Crow
Rosalie Solow Professor of Modern Art, Institute of Fine Arts, New York University
April 10, 2015
Crow examines the displaced and wandering existences of Jacques-Louis David and Théodore Géricault, both in geographical and psychological exile, during which each was forced to reexamine and reconfigure the fundamentals of his artistic life. The lecture is the third in the series of talks under the theme of “Restoration as Event and Idea: Art in Europe, 1814–1820” which is part of the sixty-fourth A.W. Mellon Lectures in the Fine Arts at the National Gallery of Art. This event is sponsored by the Friends of the Institute.

A new approach to the sensitivity conjecture

Michael Saks
Rutgers University
April 13, 2015
The sensitivity conjecture is a major outstanding foundational problems about boolean functions is the sensitivity conjecture. In one of its many forms, it asserts that the degree of a boolean function (i.e. the minimum degree of a real polynomial that interpolates the function) is bounded above by some fixed power of its sensitivity (which is the maximum vertex degree of the graph defined on the inputs where two inputs are adjacent if they differ in exactly one coordinate and their function values are different).

Quadratic families of elliptic curves and unirationality of degree 1 conic bundles

János Kollár
Princeton University
April 13, 2015
We consider elliptic curves whose coefficients are degree 2 polynomials in a variable $t$. We prove that for infinitely many values of $t$ the resulting elliptic curve has rank at least 1. All such curves together form an algebraic surface which is birational to a conic bundle with 7 singular fibers. The main step of the proof is to show that such conic bundles are unirational. (joint work with M. Mella)

Embedding the derived category of a curve into a Fano variety

Alexander Kuznetsov
Steklov Mathematical Institute, Moscow
April 14, 2015
According to the conjecture of Bondal, the derived category of coherent sheaves on any smooth projective variety can be embedded as a semiorthogonal component into the derived category of a Fano variety of higher dimension. I will explain how this embedding can be constructed for general curves of arbitrary genus. This is a joint work with Anton Fonarev.

Factorization of birational maps on steroids

Dan Abramovich
Brown University
April 14, 2015
Searching literature you will find the following statement (I'm paraphrasing): "If $X_1,X_2$ are nonsingular schemes proper over a complete DVR $R$ with residue characteristic 0, and $\phi: X_1 \to X_2$ is birational, then $\phi$ can be factored as a sequence of blowups and blowdown between nonsingular schemes proper over $R$, with nonsingular blowup centers." along with a demonstration: "The method of [Włodarczyk] or [AKMW] works word-for-word." In revenge you will find elsewhere (I'm paraphrasing): "Since a proof of weak factorization of birational maps over a complete D

Syzygies, gonality and symmetric products of curves

Robert Lazarsfeld
Stony Brook University
April 14, 2015
In the mid 1980s, Mark Green and I conjectured that one could read off the gonality of an algebraic curve $C$ from the syzygies among the equations defining any one sufficiently positive embedding of $C$. Ein and I recently noticed that a small variant of the ideas used by Voisin in her work on canonical curves leads to a quick proof of this gonality conjecture. The proof involves the geometry of certain vector bundles on the symmetric product of $C$.

Of Particles, Stars, and Eternity

Cédric Villani
Université Lyon and Institut Henri Poincaré
April 14, 2015
Can one predict the future arrangements of planets over extremely large time periods? For centuries this issue has triggered dreams of curious people, and hot debates by specialists including Newton, Lagrange, Poincare, Kolmogorov, Laskar, and Tremaine. Villani explores the long time behavior of a plasma, evoking the advances which he made with Mouhot a few years ago, and continuing with the subject of long time stability for incompressible fluids.