Abstract: It is well known that the Hilbert schemes of points on smooth surfaces are smooth. In higher dimensions the Hilbert schemes of points are in general singular. In this talk we will present some examples and conjectures on the local structures of the Hilbert scheme of points on $\mathbb{P}^3$. As an application we study a […]
Speaker: Karim Adiprasito, Hebrew University and University of Copenhagen Title: Anisotropy, biased pairing theory and applications Abstract: Not so long ago, the relations between algebraic geometry and combinatorics were strictly governed by the former party, with results like log-concavity of the coefficients of the characteristic polynomial of matroids shackled by intuitions and techniques from projective algebraic […]
https://youtu.be/rRGh97sOtKE Speaker: Patrick Massot, Laboratoire de Mathématiques d’Orsay and CNRS Title: Why explain mathematics to computers? Abstract: A growing number of mathematicians are having fun explaining mathematics to computers using proof assistant softwares. This process is called formalization. In this talk I’ll describe what formalization looks like, what kind of things it teaches us, and […]
Abstract: The gravitational dual to the grand canonical ensemble of a large N holographic theory is a charged black hole. These spacetimes can have Cauchy horizons that render the classical gravitational dynamics of the black hole interior incomplete. We show that a (spatially uniform) deformation of the CFT by a neutral scalar operator generically leads to […]
Abstract: During development, organisms interact with their natural habitats while undergoing morphological changes, yet we know little about how the interplay between developing systems and their environments impacts animal morphogenesis. Cnidaria, a basal animal lineage that includes sea anemones, corals, hydras, and jellyfish, offers unique insight into the development and evolution of morphological complexity. In my […]
Speaker: Jie Yang, Delft University of Technology Title: ARCH: Know What Your Machine Doesn’t Know Abstract: Despite their impressive performance, machine learning systems remain prohibitively unreliable in safety-, trust-, and ethically sensitive domains. Recent discussions in different sub-fields of AI have reached the consensus of knowledge need in machine learning; few discussions have touched upon the diagnosis […]
Speaker: Freid Tong Title: The complex Monge-Ampere equation in Kahler geometry Abstract: The complex Monge-Ampere equations occupies an central role in K\”ahler geometry, beginning with Yau’s famous solutions of the Calabi conjecture. Later developments has led to many interesting geometric applications and opening of new fields. In this talk, I will introduce the complex Monge-Ampere equation […]
Speaker: Eric Sharpe (Virginia Tech) Title: Anomaly resolution via decomposition Abstract: In this talk we will discuss a method of anomaly resolution due to Wang-Wen-Witten in the special case of (1+1) dimensional theories. Briefly, for our purposes, Wang-Wen-Witten argued that an ill-defined anomalous orbifold could be resolved by extending G to a larger group and […]
Speaker: Biao Lian (Princeton) Title: Integrability and chaos of 1+1d chiral edge states Abstract: I will talk about the integrability and chaos of 1+1d interacting chiral edge states, which may arise on the edge of 2+1d topological phases. We show that integrable chiral Luttinger liquid is not always a good low energy description of the […]
Speaker: Pieter Bomans, Princeton Title: Bubble instability of mIIA on AdS_4 x S^6 Abstract: Recently, a set of non-supersymmetric AdS_4 vacua of massive type IIA string theory has been constructed. These vacua are perturbatively stable with respect to the full KK spectrum of type mIIA supergravity and furthermore, they are stable against a variety of […]
Abstract: Gopakumar-Vafa invariants are integers n_beta(g) which give a virtual count of genus g curves in the class beta on a Calabi-Yau threefold. In this talk, I will give a general overview of two of the sheaf-theoretic approaches to defining these invariants: via stable pairs a la Pandharipande-Thomas (PT) and via perverse sheaves a la Maulik-Toda […]
Abstract: We consider the moduli space of abelian varieties with two marked points and a frame of the relative de Rham cohomology with boundary at these points compatible with its mixed Hodge structure. Such a moduli space gives a natural algebro-geometric framework for higher genus quasi Jacobi forms of index zero and their differential equations […]