# Seminars & Events for 2017-2018

##### Uniqueness of blow-ups and asymptotic decay for Dirichlet energy minimizing multi-valued functions

***Please note special date and time. **In the early 1980's Almgren developed a theory of Dirichlet energy minimizing multi-valued functions, proving that the Hausdorff dimension of the singular set (including branch points) of such a function is at most (n-2) where n is the dimension of its domain.

##### Noether-Lefschetz locus on singular threefolds

The classical Noether-Lefschetz theorem says that any curve in a very general surface X in P^3 of degree d \geq 4 is a restriction of a surface in the ambient space, in particular the Picard number of X is 1 (a property is very general if it holds in the complement of countably many proper closed subvarieties).

##### Joint Equidistribution of CM Points

A celebrated theorem of Duke states that Picard/Galois orbits of CM points on a complex modular curve equidistribute in the limit when the absolute value of the discriminant goes to infinity.

##### Stochastic homogenization: renormalization, regularity, and quantitative estimates

There has been a lot of work in recent years on the problem of understanding the behavior of solutions of PDEs with random coefficients, with most of the work focused on linear elliptic equations in divergence form.

##### TBA-Yu-Shen Lin

##### Two problems involving breakup of a liquid film

Understanding the breakup of a liquid film is complicated by the fact that there is no obvious instability driving breakup: surface tension favors a film of uniform thickness over a deformed one. Here, we identify two mechanisms driving a film toward (infinite time) pinch-off.

##### TBA-Xudong Zheng

##### TBA - Dr. Efi Efrati

##### TBA-Gal Mishne

##### TBA-Timo Seppalainen

##### Regularity of area-minimizing surfaces in higher codimension: old and new

The theory of integral currents, developed by Federer and Fleming in the 60s, gives a powerful framework to solve the Plateau's problem in every dimension and codimension. The interior and boundary regularity theory for the codimension

one case is rather well understood, thanks to the work of several mathematicians in the 60es, 70es and 80es.

##### TBA-Amina Abdurrahman

##### TBA-Joel Moreira

##### TBA-Suyoung Choi

##### Locally symmetric spaces: p-adic aspects

p-adic period spaces have been introduced by Rapoport and Zink as a generaliza- tion of Drinfeld upper half spaces and Lubin-Tate spaces. Those are open subsets of a rigid analytic p-adic flag manifold. An approximation of this open subset is the so called weakly admissible locus obtained by removing a profinite set of closed Schubert varieties.

##### TBA-Serguei Denissov

##### Irreducible SL(2,C)-representations of integer homology 3-spheres

We prove that the splicing of any two non-trivial knots in the 3-sphere admits an irreducible SU(2)-representation of its fundamental group. This uses instanton gauge theory, and in particular a non-vanishing result of Kronheimer-Mrowka and some new results that we establish for holonomy perturbations of the ASD equation.

##### TBA-Maria Colombo

##### Attractors: "when inertial waves meet topography..."

##### Bulk-Edge Duality and Complete Localization for Chiral Chains

We study one dimensional insulators obeying a chiral symmetry in the single-particle picture where the Fermi energy is assumed to lie within a mobility gap. Topological invariants are defined for infinite (bulk) or half-infinite (edge) systems, and it is shown that for a given bulk system with nearest neighbor hopping, the invariant is equal to the induced-edge-system's invariant.