Related papers: Intrinsic Mirrors for Minimal Adjoint Orbit (ICM G…

We investigate the rudiments of Riemannian geometry on orbit spaces $M/G$ for isometric proper actions of Lie groups on Riemannian manifolds. Minimal geodesic arcs are length minimising curves in the metric space $M/G$ and they can hit…

These are lecture notes compiled for a short lecture series at the 2023 Condensed Matter Summer School at the University of Minnesota. They are designed to be conversational and fun, and not to take the place of review articles that do a…

These notes are loosely based on an introductory course in algebraic geometry given at Rutgers University in Spring of 2024. We introduce some relatively advanced topics at the expense of the technical details.

This proceedings note introduces aspects of the authors' work relating mirror symmetry and integral variations of Hodge structure. The emphasis is on their classification of the integral variations of Hodge structure which can underly…

Inspired by the paper on quantum knots and knot mosaics [23] and grid diagrams (or arc presentations), used extensively in the computations of Heegaard-Floer knot homology [2,3,7,24], we construct the more concise representation of knot…

We study framed surfaces, which are a class of Euclidean minimal and hyperbolic CMC-1 surfaces that generalize immersed minimal surfaces in $\mathbb{R}^3$ and Bryant surfaces. For this class we prove a lower bound on the (unrestricted)…

This survey of recent developments in cloaking and transformation optics is an expanded version of the lecture by Gunther Uhlmann at the 2008 Annual Meeting of the American Mathematical Society.

This short introduction to positive geometries, targeted at a mathematical audience, is based on my talk at OPAC 2022.

We generalize the exact field theoretic correspondence proposed in arXiv:1103.5726 and embed it into the context of refined topological string. The correspondence originally proposed from the common integrable structures in different field…

ICM lecture on minimal models and moduli of varieties.

This note is based on a lecture delivered by the author at the Second Conference on Differential Geometry, held in Fez in October 2024. It offers an accessible introduction to biharmonic and biconservative submanifolds, exploring the…

This paper presents the computational challenge on differential geometry and topology that happened within the ICLR 2021 workshop "Geometric and Topological Representation Learning". The competition asked participants to provide creative…

Recently, Honda, Kazez and Matic described an adapted partial open book of a compact contact 3-manifold with convex boundary by generalizing the work of Giroux in the closed case. They also implicitly established a one-to-one correspondence…

These are lecture notes on Floer and Rabinowitz-Floer homology written for a graduate course at UNICAMP August-December 2016 and a mini-course held at IMPA in August 2017.

These are the notes for a series of lectures at the Institute of Geometry and Topology of the University of Stuttgart, Germany, in July 13-15, 2022. We assume basic knowledge of isometric actions on Riemannian manifolds, including the…

We study the open/closed correspondence for the projective line via mirror symmetry. More explicitly, we establish a correspondence between the generating function of disk Gromov-Witten invariants of the complex projective line…

This paper will appear in the Proceedings of the 1995 Santa Cruz Summer Institute. The paper is a survey of recent developments in the theory of toric varieties, including new constructions of toric varieties and relations to symplectic…

The geometric aspects of mirror symmetry are reviewed, with an eye towards future developments. Given a mirror pair (X,Y) of Calabi-Yau threefolds, the best-understood mirror statements relate certain small corners of the moduli spaces of X…

We demonstrate the existence of topological insulators in one dimension protected by mirror and time-reversal symmetries. They are characterized by a nontrivial $\mathbb{Z}_2$ topological invariant defined in terms of the "partial"…

We report on recent progress in understanding mirror symmetry. Some of more recent generalizations and applications are also presented. --- A contribution to the Proceedings of ``Strings 2001'' at Mumbai, India.