# Seminars & Events for 2017-2018

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

##### Foliated surfaces and their stable reduction.

In 1977 Bogomolov proved that on surfaces of general type with c_1^2>c_2, curves of a given genus form a bounded family. The role played by foliations in his proof was further investigated by McQuillan, who in 1998 proved the Green-Griffiths conjecture for surfaces of general type with c_1^2>2c_2.

##### 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.

##### TBA-Jun Su

##### Reconstructing 3D protein crystal intensity from unoriented sparse diffraction patterns

The femtoseconds long pulses of an X-ray free electron laser (XFEL) enable the measurement to outrun the irreversible radiation damage. This concept of `diffract before destroy’ inspires new methods such as serial crystallography, which determines 3D protein structures by merging 2D snapshots of microcrystals collected at random orientations.

##### The Kuga-Satake construction.

The Kuga-Satake construction associates an abelian variety (the Kuga-Satake variety) to certain weight two Hodge structure, for example the second cohomology group of a K3 surface. I will discuss the construction, and its applications to the Weil conjecture, the Hodge conjecture, and the Tate conjecture (related to K3 surfaces).

##### From counting Markoff triples to Apollonian packings; a path via elliptic K3 surfaces and their ample cones

The number of integer Markoff triples below a given bound has a nice asymptotic formula with an exponent of growth of 2. The exponent of growth for the Markoff-Hurwitz equations, on the other hand, is in generalnot an integer. Certain elliptic K3 surfaces can be thought of as smooth generalizations of the Markoff surface. Like the Markoff surface, their group of automorphisms is discrete and

##### TBA-Gautam Iyer

##### Chern-Simons functional and the Homology Cobordism Group

The set of 3-manifolds with the same homology as the 3-dimensional sphere, modulo an equivalence relation called *homology cobordance*, forms a group.

##### TBA-Cary Malkiewich

##### Ruixiang Zhang

##### TBA-Lenny Ng

##### Quasi-resonant forcing: "how generalized eigenfunctions can be observed in a bowl..."

##### Explicit equations of a fake projective plane.

Fake projective planes are complex algebraic surfaces of general type whose Betti numbers are the same as that of a usual projective plane. The first example was constructed by Mumford about