相关论文: Lectures on flips and minimal models

These are notes of a mini-course given at Dennisfest in June 2001. The goal of these notes is to give a self-contained survey of deformation quantization, operad theory, and graph homology. Some new results related to "String Topology" and…

These lecture notes consist of an introduction to moduli spaces in algebraic geometry, with a strong emphasis placed on examples related to the theory of quiver representations. The goal is to provide the background necessary to understand…

These are the notes for the lecture given by the author at the "Current Events" Special Session of the AMS meeting in Baltimore on January 17, 2003. Topics reviewed include the Langlands correspondence for GL(n) in the function field case…

This is an expanded version of my plenary lecture at the 8th European Congress of Mathematics in Portoro\v{z} on 23 June 2021. The main part of the paper is a survey of recent applications of complex-analytic techniques to the theory of…

This is an expanded version of the notes of my three lectures at a NATO Advanced Study Institute ``Symmetric functions 2001: surveys of developments and perspectives" (Isaac Newton Institute for Mathematical Sciences, Cambridge, UK; June…

We explicitly provide minimal Gr\"obner bases for simple, finite-dimensional modules of complex Lie algebras of types A and C, using a homogeneous ordering that is compatible with the PBW filtration on the universal enveloping algebras.

We prove that for any two minimal models of an lc algebraically integrable foliated triple on potentially klt varieties, there exist small birational models that are connected by a sequence of flops. In particular, any two minimal models of…

An article based on a four-lecture introductory minicourse on minimal surface theory given at the 2013 summer program of the Institute for Advanced Study and the Park City Mathematics Institute.

These are notes from an informal mini-course on factorization homology, infinity-categories, and topological field theories. The target audience was imagined to be graduate students who are not homotopy theorists.

These are notes from the mini-course given by W. Schmid in June 2003 in the Brussels PQR2003 Euroschool.

This short expository note gives an elementary introduction to the study of dynamics on certain moduli spaces, and in particular the recent breakthrough result of Eskin, Mirzakhani, and Mohammadi. We also discuss the context and…

Hassett and Keel predicted that there is a descending sequence of critical $\alpha$ values where the log canonical model for the moduli space of stable curves with respect to $\alpha \delta$ changes. We derive a conjectural formula for the…

Compactifications of moduli spaces of (1,p)-polarized abelian surfaces with level structures of canonical type have been described in great detail by Hulek, Kahn and Weintraub. The aim of this paper is to determine some invariants of smooth…

We present new geometric formulations for the fractional spin particle models on the minimal phase spaces. New consistent couplings of the anyon to background fields are constructed. The relationship between our approach and previously…

More than 10 years ago, Dipper, James and Murphy developped the theory of Specht modules for Hecke algebras of type $B\_n$. More recently, using Lusztig's a-function, Geck and Rouquier showed how to obtain parametrisations of the…

We survey a number of recent developments in geometric analysis as they pertain to the calculus of variations and extremal problems in geometric function theory following the NZMRI lectures given by the first author at those workshops in…

In this paper we considerably extend the class of known $\alpha$-minimizing hypercones using sub-calibration methods. Indeed, the improvement of previous results follows from a careful analysis of special cubic and quartic polynomials.

This is a first graduate course in algebraic geometry. It aims to give the student a lift up into the subject at the research level, with lots of interesting topics taken from the classification of surfaces, and a human-oriented discussion…

These are lecture notes for a 4h mini-course held in Toulouse, May 9-12th, at the thematic school on "Quantum topology and geometry". The goal of these lectures is to (a) explain some incarnations, in the last ten years, of the idea of…

Notes of three talks given at the workshop 'Hilbert schemes, non-commutative algebra and the McKay correspondence' CIRM-Luminy (France) October 2003. If A is an order over a central normal affine variety X having a stability structure such…