# Department of **Mathematics**

## Directory

## Matthew Ballard

Title: |
Professor |

Department: |
Mathematics College of Arts and Sciences |

Email: |
ballard@math.sc.edu |

Phone: |
803-777-7529 |

Office: |
LeConte 341 |

Resources: |
My Website Curriculum Vitae [pdf] Department of Mathematics |

#### Education

BS, Mathematics, California Institute of Technology, 2002

PhD, Mathematics, University of Washington, 2008

#### Experience

2022-current, Professor, University of South Carolina

2018-2021, Associate Professor, University of South Carolina2016-2017, Member, Institute for Advanced Study

2013-2017, Assistant Professor, University of South Carolina

2012-2013, Senior Researcher, University of Vienna

2011-2012, Van Vleck Visiting Assistant Professor, University of Wisconsin

2008-2011, Postdoctoral Researcher, University of Pennsylvania

2013-2017, Assistant Professor, University of South Carolina

2012-2013, Senior Researcher, University of Vienna

2011-2012, Van Vleck Visiting Assistant Professor, University of Wisconsin

2008-2011, Postdoctoral Researcher, University of Pennsylvania

#### Courses Taught

Math 141, Calculus IMath 142, Calculus IIMath 241, Calculus IIIMath 300, Transition to Advanced MathematicsMath 544, Linear AlgebraMath 546, Algebraic StructuresMath 701, Algebra IMath 702, Algebra IIMath 732, Algebraic Topology IMath 733, Algebraic Topology IIMath 737, Complex Geometry IMath 738, Derived Categories I (Fall 2021)Math 748, Derived Categories II (Spring 2022)

#### Honors and Awards

2019-2021 UofSC College of Arts and Sciences Teaching Incubator Associate, 2018 UofSC Breakthrough Star, Invited lecture at 2015 Summer Institute in Algebraic Geometry at the University of Utah, Plenary speaker at String-Math 2014.

#### Research

I am an algebraic geometer who uses the tools around derived categories to solve problems
with ties to number theory, commutative and noncommutative algebra, representation
theory, theoretical physics, and symplectic geometry. My recent work studies the derived geometry of birational maps, analyzes the relationship
between rationality and derived categories over general fields, and develops derived
approaches to noncommutative algebraic geometry. My research has been supported by
the National Science Foundation and the Simons Foundation. I have lectured on my work
at over 40 institutions, on 4 continents, including Cornell, Princeton, Yale, the
IAS, MSRI, the Fields Institute, BIRS, and the MFO. arXiv. Google Scholar. orcid.org/0000-0001-5819-0159.

#### Selected Publications

- Matthew Ballard, David Favero and Ludmil Katzarkov. Variation of Geometric Invariant Theory quotients and derived categories Journal für die reine und angewandte Mathematik (Crelle). Issue 746 (2019) 235--304. DOI:10.1515/crelle-2015-0096
- Matthew Ballard. Wall crossing for derived categories of moduli spaces of sheaves on rational surfaces. Algebraic Geometry 4 (3) (2017) 263--280. DOI:10.14231/AG-2017-014
- Matthew Ballard, Dragos Deliu, David Favero, M. Umut Isik, and Ludmil Katzarkov. Homological Projective Duality via variation of Geometric Invariant Theory quotients. Journal of the European Mathematical Society. Volume 19 Issue 14 (2017) 1127-1158. DOI:10.4171/JEMS/689
- Matthew Ballard, David Favero and Ludmil Katzarkov. A category of kernels for equivariant factorizations and its implications for Hodge theory, I. Publications mathématiques de l'IHÉS 120 (2014), no. 1, 1-111. DOI:10.1007/s10240-013-0059-9
- Matthew Ballard, David Favero and Ludmil Katzarkov. Orlov spectra: bounds and gaps Inventiones Mathematicae 189 (2012), no. 2, 359-430. DOI:10.1007/s00222-011-0367-y