## On structure results for intertwining operators

## Applications of twisted technology

Recently we proved with Durcik, Kovac, Skreb variational estimates providing sharp quantitative norm convergence results for bilinear ergodic averages with respect to two commuting transformations. The proof uses so called twisted technology developed in recent years for estimating bi-parameter paraproducts. Another application of the technique is to cancellation results for simplex Hilbert transforms.

## Homological mirror symmetry for the pair of pants

## 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.