Title: The Kervaire conjecture and the minimal complexity of surfaces Abstract: We use topological methods to solve special cases of a fundamental problem in group theory, the Kervaire conjecture. The conjecture asserts that, for any nontrivial group G and any element w in the free product G*Z, the quotient (G*Z)/<<w>> is still nontrivial. We interpret this […]
Title: Amplituhedra, Scattering Amplitudes and Triangulations Abstract: In this talk I will discuss about Amplituhedra – generalizations of polytopes inside the Grassmannian – recently introduced by physicists as new geometric constructions encoding interactions of elementary particles in certain Quantum Field Theories. In particular, I will explain how the problem of finding triangulations of Amplituhedra is connected to […]
Title: Polyhomogeneous expansions and Z/2-harmonic spinors branching along graphs Abstract: In this talk, we will first reformulate the linearization of the moduli space of Z/2-harmonic spinorsv branching along a knot. This formula tells us that the kernel and cokernel of the linearization are isomorphic to the kernel and cokernel of the Dirac equation with a polyhomogeneous boundary […]
Title: Numerical Higher Dimensional Geometry Abstract: In 1977, Yau proved that a Kahler manifold with zero first Chern class admits a Ricci flat metric, which is uniquely determined by certain “moduli” data. These metrics have been very important in mathematics and in theoretical physics, but despite much subsequent work we have no analytical expressions for them. But […]
Title: Quadratic reciprocity from a family of adelic conformal field theories Abstract: We consider a deformation of the 2d free scalar field action by raising the Laplacian to a positive real power. It turns out that the resulting non-local generalized free action is invariant under two commuting actions of the global conformal symmetry algebra, although it’s no […]
Speaker: Boyu Zhang, Princeton University Title: The smooth closing lemma for area-preserving surface diffeomorphisms Abstract: In this talk, I will introduce the smooth closing lemma for area-preserving diffeomorphisms on surfaces. The proof is based on a Weyl formula for PFH spectral invariants and a non-vanishing result of twisted Seiberg- Witten Floer homology. This is joint work […]
Title: Markov chains, optimal control, and reinforcement learning Abstract: Markov decision processes are a model for several artificial intelligence problems, such as games (chess, Go…) or robotics. At each timestep, an agent has to choose an action, then receives a reward, and then the agent’s environment changes (deterministically or stochastically) in response to the agent’s action. […]
Title: Polynomials vanishing at lattice points in convex sets Abstract: Let P be a convex subset of R^2. For large d, what is the smallest degree r_d of a polynomial vanishing at all lattice points in the dilate d*P? We show that r_d / d converges to some positive number, which we compute for many (but maybe not […]
Title:Quasiperiodic prints from triply periodic blocks Abstract: Slice a triply periodic wooden sculpture along an irrational plane. If you ink the cut surface and press it against a page, the pattern you print will be quasiperiodic. Patterns like these help physicists see how metals conduct electricity in strong magnetic fields. I’ll show you some block prints […]
Title: Metric Algebraic Geometry Abstract: A real algebraic variety is the set of points in real Euclidean space that satisfy a system of polynomial equations. Metric algebraic geometry is the study of properties of real algebraic varieties that depend on a distance metric. In this talk, we introduce metric algebraic geometry through a discussion of Voronoi […]
Abstract: Finite order Markov models are theoretically well-studied models for dependent data. Despite their generality, application in empirical work when the order is larger than one is quite rare. Practitioners avoid using higher order Markov models because (1) the number of parameters grow exponentially with the order, (2) the interpretation is often difficult. Mixture of transition […]
Abstract: In this talk we describe a new method to study the singular set in the obstacle problem. This method does not depend on monotonicity formulae and works for fully nonlinear elliptic operators. The result we get matches the best-known result for the case of Laplacian.