Arend Bayer

University of Connecticut, Department of Mathematics

Room 206
Office phone: (860) 486-4237

arend.bayer@uconn.edu

I am Assistant Professor (tenure track) at the University of Connecticut since Fall 2009. A CV.

Teaching

Currently I am teaching Geometry from derived categories (Topics in Geometry).

Previously, I have taught: In the Fall Semester 2011: Introduction to Algebraic Geometry and Geometry (2360Q). In the Fall Semester 2010: Introduction to Topology and Geometry and Honors Calculus II. In the Spring Semester 2010: Applied Linear Algebra (2210Q) and Algebraic Geometry 2 (5031); In Fall Sememster 2009: Multivariable Calculus (2110Q) and Probability (3160).

Research interests

Algebraic Geometry motivated by string theory:

My research has been supported by NSF grants since 2008 (DMS 0801356 and DMS 1101377).

Publications and preprints

Joint with Emanuele Macrì:Projectivity and birational geometry of Bridgeland moduli spaces.arXiv:1203.4613.

Joint with Aaron Bertram, Emanuele Macrì and Yukinobu Toda:Bridgeland Stability conditions on Threefolds II: An application to Fujita's conjecture. arXiv:1106.3430.

Joint with Emanuele Macrì and Yukinobu Toda:Bridgeland Stability conditions on Threefolds I: Bogomolov-Gieseker type inequalities. arXiv:1103.5010.

Joint with Emanuele Macrì:The space of stability conditions on the local projective plane. arXiv:0912.0043. Some related SAGE code. Duke Math. J. 160 (2011) no. 2, 263–322.

Polynomial Bridgeland stability conditions and the large volume limit. arXiv:0712.1083. Geometry & Topology 13 (2009), no. 4, 2389-2425.

Joint with Charles Cadman: Quantum Cohomology of [C^N/mu_r]. arXiv:0705.2160. Compos. Math. 146 (2010), no. 5, 1291–1322.

Joint with Yuri I. Manin: Stability conditions, wall-crossing and weighted Gromov-Witten invariants. arXiv:math.AG/0607580. Mosc. Math. J. 9 (2009), no. 1, 3-23.

Semisimple quantum cohomology and blowups. Int. Math. Res. Not. 2004, no. 40, 2069--2083. math.AG/0403260.

Joint with Yuri I. Manin: (Semi)simple Exercises in Quantum Cohomology. The Fano Conference, 143--173, Univ. Torino, Turin, 2004. math.AG/0103164

Lecture notes

Here are brief lecture notes on Bridgeland stability conditions intended for graduate students interested in the topic.

Graduate students

Rebecca Tramel.

Theses

My PhD thesis on "Semisimple Quantum Cohomology, deformations of stability conditions and the derived category", written under supervision of Yuri I. Manin.

My diploma thesis on "Semisimple Frobenius Manifolds and Quantum Cohomology", also supervised by Yuri I. Manin.

My essay (for the exams of "Part III" in Cambridge) on "Mirror Symmetry for the Elliptic Curve", written under supervision by Alessio Corti.

AGNES

The Algebraic Geometry Northeastern Series (AGNES) is a series of algebraic geometry workshops in the Northeast, meeting twice a year since 2009. The next UConn workshop is expected to take place in the Fall 2013.