The Hull-Strominger system is a system of nonlinear PDEs describing the geometry of compactification of heterotic strings with torsion to 4d Minkowski spacetime, which can be regarded as a generalization of Ricci-flat Kähler metrics coupled with Hermitian Yang-Mills equation on non-Kähler Calabi-Yau 3-folds. The Anomaly flow is a parabolic approach to understand the Hull-Strominger system initiated by Phong-Picard-Zhang. We show that in the setting of generalized Calabi-Gray manifolds, the Hull-Strominger system and the Anomaly flow reduce to interesting elliptic and parabolic equations on Riemann surfaces. By solving these equations, we obtain solutions to the Hull-Strominger system on a class of compact non-Kähler Calabi-Yau 3-folds with infinitely many topological types and sets of Hodge numbers. This talk is based on joint work with Zhijie Huang and Sebastien Picard.

In this talk, I will discuss a direction of study in topology: Section problems. There are many variations of the problem: Nielsen realization problems, sections of a surface bundle, sections of a bundle with special property (e.g. nowhere zero vector eld). I will discuss some techniques including homology, Thurston-Nielsen classication and dynamics. Also I will share many open problems. Some of the result are joint work with Nir Gadish, Justin Lanier and Nick Salter.

Hierarchically hyperbolic spaces provide a uniform framework for working with many important examples, including mapping class groups, right angled Artin groups, Teichmuller space, and others. In this talk I'll provide an introduction to studying groups and spaces from this point of view. This discussion will center around recent work in which we classify quasiflats in these spaces, thereby resolving a number of well-known questions and conjectures. This is joint work with Mark Hagen and Alessandro Sisto.

It is a classical topic dating back to Maclaurin (1698–1746) to study certain special points on smooth cubic plane curves, such as the 9 inflection points (Maclaurin and Hesse), the 27 sextatic points (Cayley), and the 72 points "of type 9" (Gattazzo). Motivated by these algebro-geometric constructions, we ask the following topological question: is it possible to choose n distinct points on a smooth cubic plane curve as the curve varies continuously in family, for any integer n other than 9, 27 and 72? We will present both constructions and obstructions to such continuous choices of points, state a classification theorem for them, and discuss conjectures and open questions.

Seidel's Lagrangian Dehn twist exact sequence has been a
cornerstone of the theory of Fukaya categories.  In the last decade,
Huybrechts and Thomas discovered a new autoequivalence in the derived
cateogry of coherent sheaves using the so-called "projective objects", which
are presumably mirrors of Lagrangian projective spaces.   On the other hand,
Seidel's construction of Lagrangian Dehn twists as symplectomorphisms can be
easily generalized to Lagrangian projective spaces.  The induce
auto-equivalence on Fukaya categories are conjectured to be the mirror of
Huybrechts-Thomas's auto-equivalence on B-side.  

This remains open until recently, and I will explain my joint work with
Cheuk-Yu Mak on the solution to this conjecture using the technique of
Lagrangian cobordisms.  Moreover, we will explain a recent progress, again
joint with Cheuk-Yu Mak, on pushing this further to Lagrangian embeddings of
finite quotients of rank-one symmetric spaces, leading to another new class
of auto-equivalences, which are different from the classical spherical
twists only in coefficients of finite characteristics.