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.

Reflections on Inequality and Capital in the 21st Century

Thomas Piketty
EHESS and Paris School of Economics
May 12, 2017
In this public lecture, Thomas Piketty will present new findings and reflections on global inequality dynamics. In particular, he will stress the need to go beyond the Western-centered historical perspective on inequality regimes developed in his book, Capital in the 21st Century. Piketty will also address the relation between rising inequality and the changing structure of electoral conflict, from class-based to identity-based conflict.

The $p$-curvature conjecture and monodromy about simple closed loops

Ananth Shankar
Harvard University
May 11, 2017
The Grothendieck-Katz $p$-curvature conjecture is an analogue of the Hasse Principle for differential equations. It states that a set of arithmetic differential equations on a variety has finite monodromy if its $p$-curvature vanishes modulo $p$, for almost all primes $p$. We prove that if the variety is a generic curve, then every simple closed loop has finite monodromy.

String topology coproduct: geometric and algebraic aspects

Manuel Rivera
University of Miami
May 11, 2017
The string topology coproduct is an intersection type operation, originally described by Goresky-Hingston and Sullivan, which considers transverse self-intersections on chains of loops in a smooth manifold and splits loops at these intersection points. The geometric chain level construction of string topology operations involves deforming chains to achieve certain transversality conditions and these deformations introduce higher homotopy terms for algebraic compatibilities and properties.

Floer theory in spaces of stable pairs over Riemann surfaces

Timothy Perutz
University of Texas, Austin; von Neumann Fellow, School of Mathematics
May 4, 2017
I will report on joint work with Andrew Lee, which explores the notion that spaces of stable pairs over Riemann surfaces (in the sense of Bradlow and Thaddeus) could form a natural home for a “non-abelian” analog of Heegaard Floer homology for 3-manifolds - just as the g-fold symmetric product is the home of Heegaard Floer homology - thereby circumventing the problems with singularities that beset instanton-type theories. In an initial foray into this area, we set up a theory not for Heegaard splittings but for fibered 3-manifolds, based on fixed-point Floer homology.

Lagrangian Floer theory in symplectic fibrations

Douglas Schultz
Rutgers University
April 27, 2017
Given a fibration of compact symplectic manifolds and an induced fibration of Lagrangians, one can ask if we can compute the Floer cohomology of the total Lagrangian from information about the base and fiber Lagrangians. The primary example that we have in mind is the manifold of full flags in ${\mathbb C}^3$ which fibers as ${\mathbb P}^1 \to {\rm Flag}({\mathbb C}^3) \to {\mathbb P}^2$, and a Lagrangian $T^3$ that fibers over the Clifford torus in ${\mathbb P}^2$.

Albert Hirschman Award Ceremony and Program

featuring Peter Lange, Duke University; Didier Fassin, Institute for Advanced Study; and Ira Katznelson, Social Science Research Council
April 19, 2017
Albert O. Hirschman Prize Ceremony and Program
Please join the Social Science Research Council and the Institute for Advanced Study for the Albert O. Hirschman Prize Ceremony and Program honoring Amartya Sen.
featuring Peter Lange, Duke University; Didier Fassin, Institute for Advanced Study; and Ira Katznelson, Social Science Research Council
April 19, 2017 at 5 p.m.
Institute for Advanced Study, Wolfensohn Hall