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Department of Mathematics


Matthew Ballard

Title: Professor
Department: Mathematics
College of Arts and Sciences
Phone: 803-777-7529
Office: COL 1022C
Office Hours: TR 7:45-8:30 and 11:30-12:15
Resources: My Website 
Curriculum Vitae [pdf]
Department of Mathematics
Matthew Ballard


BS, Mathematics, California Institute of Technology, 2002
PhD, Mathematics, University of Washington, 2008


2022-current, Professor, University of South Carolina
2018-2021, Associate Professor, University of South Carolina
2016-2017, 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

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. 


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. arXivGoogle   

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

Challenge the conventional. Create the exceptional. No Limits.