## Applications of monotone constraint satisfaction

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.

## Extremal problems in combinatorial geometry

## Applications of monotone constraint satisfaction

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.

## Continuous covers on symplectic manifolds

## The simplification of caustics

## Towards homological mirror symmetry for complete intersections in toric varieties

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

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

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

## Lattices, Filtrations and some Applications

from a new prospective. Applications to geometry will be considered.