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.

Applications of monotone constraint satisfaction

Robert Robere
University of Toronto
March 28, 2017

Recently, a certain "monotone" version of the constraint satisfaction problem has proved an extremely useful tool for attacking problems in circuit, communication, and proof complexity theory. In this talk we discuss this version of the constraint satisfaction problem and touch on its connection to fundamental lower-bounds problems in these areas. We also consider a recent and interesting application: the first exponential lower bounds on the length of cutting planes refutations of random CNF formulas.

Applications of monotone constraint satisfaction

Robert Robere
University of Toronto
March 27, 2017

Recently, a certain "monotone" version of the constraint satisfaction problem has proved an extremely useful tool for attacking problems in circuit, communication, and proof complexity theory. In this talk we discuss this version of the constraint satisfaction problem and touch on its connection to fundamental lower-bounds problems in these areas. We also consider a recent and interesting application: the first exponential lower bounds on the length of cutting planes refutations of random CNF formulas.

Towards homological mirror symmetry for complete intersections in toric varieties

Denis Auroux
IAS
March 13, 2017
Abstract: In this talk we will report on joint work in progress with Mohammed Abouzaid
concerning homological mirror symmetry for hypersurfaces in (C*)^n, namely, comparing the
derived category of the hypersurface and the Fukaya category of the mirror Landau-Ginzburg
model. We will then discuss the extension of these results to (essentially arbitrary) complete
intersections in toric Fano varieties.

Topological Fukaya categories with coefficients

Tobias Dyckerhoff
University of Bonn
March 13, 2017
Abstract: Within an emerging approach to Fukaya categories via cohomology with categorical
coefficients, I will outline a theory of a particularly nice class of nonconstant coefficient systems
defined on Riemann surfaces. These are categorical analogues of perverse sheaves, called
perverse schobers. We provide a definition of perverse schobers as categorical sheaves on a
relative two-colored version of the unital Ran space of the surface. We explain how to describe

Equivariant geometry and Calabi-Yau manifolds

Daniel Halpern-Leistner
Columbia University
March 16, 2017
Abstract: Mirror symmetry has led to deep conjectures regarding the geometry of Calabi-Yau
manifolds. One of the most intriguing of these conjectures states that various geometric
invariants, some classical and some more homological in nature, agree for any two Calabi-Yau
manifolds which are birationally equivalent to one another. I will discuss how new methods in
equivariant geometry have shed light on this conjecture over the past few years, ultimately