Matt Kerr

Cupples I, Room 114
e-mail: matkerr [at] math.wustl.edu

Recent and Upcoming Conferences:

Western Algebraic Geometry Symposium, November 4-5, 2023, St. Louis
(co-organized with R. Beheshti and W. Li)

Spectral Theory, Algebraic Geometry, and Strings, June 19-23, 2023, Mainz
(co-organized with C. Doran, A Grassi, H. Jockers and M. Mariño)

Algebraic Geometry and Algebraic K-Theory, May 23-25, 2022, St. Louis
(co-organized with R. Beheshti and J. Shareshian)

Recent advances in Hodge theory, June 10-20, 2013, Vancouver
(co-organized with J. Lewis and G. Pearlstein) photos
Summer school notes and schedule / Conference notes and schedule / Proceedings volume
Algebraic and Arithmetic Geometry seminar Instructions for Math Department Colloquium
Washington University Math Circle


Upcoming Teaching (Fall 2024):

Algebra I
Complex Analysis I

Some Course Notes:

Honors Math II
Honors Math I
Linear Algebra
Complex Analysis II
Algebraic Geometry
Hodge Theory
Algebraic cycles Number Theory and Cryptography (book)

Research:

CV updated November 2023
A brief description of some of my past work
Recent talks on Nilpotent cones, Normal functions, and Adjoint varieties
Older talks on Regulator maps, Mumford-Tate groups and Normal functions
NSF grants: Algebraic cycles, Hodge theory, and arithmetic (2011-14);
   FRG: Hodge theory, moduli, and representation theory (2014-19; FRG website);
   Asymptotic Hodge theory, fibered motives, and algebraic cycles (2021-24)
Postdoctoral associates: Ivan Horozov (2011-2015); Patricio Gallardo (2017-2019); Humberto Diaz (2019-2022); Jay Yang (2022-present)
Current Ph.D. Students: Xiaojiang Cheng; RJ Acuna; Devin Akman; Rachel Wu
Ph.D. Graduates: Ryan Keast (2016); Genival da Silva Jr. (2016); Yu Yang (2017); Muxi Li (2018); Tokio Sasaki (2019); Soumya Sinha Babu (2022); Ben Castor (2022); Haohua Deng (2022)

Publications:
  1. with R. Laza, Hodge theory of degenerations, (III): a vanishing cycle calculus for non-isolated singularities, preprint, 2023. (link)
  2. with B. Castor, H. Deng and G. Pearlstein, Remarks on eigenspectra of isolated singularities, to appear in Pacific J. Math. (2024). (link)
  3. with C. Doran and S. Sinha Babu, K2 and quantum curves, to appear in ATMP (2024). (link)
  4. with P. Gallardo, Algebraic and analytic compactifications of moduli spaces, Notices of the AMS 69 (2022), no. 9, 1476-1485. (publ. version) (arXiv version)
  5. with V. Golyshev and T. Sasaki, Apéry extensions, J. London Math. Soc. 109 (2024), no. 1, e12825. (link)
  6. Unipotent extensions and differential equations (after Bloch-Vlasenko), CNTP 16 (2022), no. 4, 801-849. (link)
  7. with R. Laza, Hodge theory of degenerations, (II): vanishing cohomology and geometric applications, preprint, 2023. (link)
  8. with P. Gallardo and L. Schaffler, Geometric interpretation of toroidal compactifications of moduli of points in the line and cubic surfaces, Adv. Math. 381 (2021), Paper No. 107632, 48 pp.(link)
  9. with R. Laza and M. Saito, Smoothing of rational singularities and Hodge structure, Algebraic Geometry 9 (2022), no. 4, 476-501.(link)
  10. with R. Laza, Hodge theory of degenerations, (I): consequences of the decomposition theorem (appendix by M. Saito), Selecta Math. 27 (2021), Paper No. 71, 48 pp. (link)
  11. with M. Li, Two applications of the integral regulator, Pacific J. Math. 306 (2020), 539-556. (link)
  12. Motivic irrationality proofs, preprint, 2020. (link)
  13. with G. Pearlstein and C. Robles, Polarized relations on horizontal SL(2)s, Documenta Math. 24 (2019), 1179-1244. (link)
  14. with P. del Angel, C. Doran, J. Iyer, J. Lewis, S. Mueller-Stach, and D. Patel, Specialization of cycles and the K-theory elevator, CNTP 13 (2019), 299-349. (link)
  15. with Y. Yang, An explicit basis for the rational higher Chow groups of abelian number fields, Ann. K-theory 3 (2018), 173-191. (link)
  16. Counting, sums, and series, preprint, 2018, to appear in ASMI volume. (pdf)
  17. with C. Robles, Variations of Hodge structure and orbits in flag varieties, Adv. Math. 315 (2017), 27-87. (link)
  18. with S. Bloch and P. Vanhove, Local mirror symmetry and the sunset Feynman integral, ATMP 21 (2017), 1373-1453. (link)
  19. with C. Robles, Classification of smooth horizontal Schubert varieties, preprint, 2016, Euro. J. Math. 3 (2017), 289-310. (link)
  20. with R. Keast, Normal functions over locally symmetric varieties, SIGMA 14 (2018), 116-133. (link)
  21. with J. Burgos Gil, J. Lewis and P. Lopatto, Simplicial Abel-Jacobi maps and reciprocity laws, J. Alg. Geom. 27 (2018), 121-172. (link)
  22. with G. da Silva Jr. and G. Pearlstein, Arithmetic of degenerating principal variations of Hodge structure: examples arising from mirror symmetry and middle convolution, Canad. J. Math. 68 (2016), 280-308. (link)
  23. with S. Bloch and P. Vanhove, A Feynman integral via higher normal functions, Compositio Math. 151 (2015), 2329-2375. (link)
  24. with I. Horozov, appendix to Reciprocity laws on algebraic surfaces via iterated integrals, J. of K-Theory 14 (2014), 304-310. (pdf)
  25. Algebraic and arithmetic properties of period maps, in "Calabi-Yau varieties: arithmetic, geometry, and physics", 173-208, Fields Inst. Monogr. 34, Toronto, ON, 2015. (pdf)
  26. with G. Pearlstein, Naive boundary strata and nilpotent orbits, Ann. Inst. Fourier 64 (2014), 2659-2714. (pdf)
  27. with C. Doran, Algebraic cycles and local quantum cohomology, CNTP 8 (2014), 703-727. (pdf)
  28. with P. Griffiths and M. Green, "Hodge Theory, Complex Geometry and Representation Theory", CBMS Regional Conference Series in Mathematics, Number 118, AMS, Providence, 2013.
  29. Cup products in automorphic cohomology: the case of Sp4, in "Hodge Theory, Complex Geometry, and Representation Theory (Doran, Friedman, Nollet, Eds.)", Contemp. Math. 608, AMS, Providence, 2014, 199-234. (pdf)
  30. Notes on the representation theory of SL2(R), in "Hodge Theory, Complex Geometry, and Representation Theory (Doran, Friedman, Nollet, Eds.)", Contemp. Math. 608, AMS, Providence, 2014, 173-198. (pdf)
  31. with J. McCarthy and O. Shalit, On the isomorphism question for complete Pick multiplier algebras, Integral Equations and Operator Theory 76 (2013), no. 1, 39-53. (link)
  32. Indecomposable K1 of elliptically fibered K3 surfaces: a tale of two cycles, in "Arithmetic and geometry of K3 surfaces and C-Y threefolds (Laza, Schuett, Yui Eds.)", Fields Inst. Comm. 67, Springer, New York, 2013, 387-409. (pdf)
  33. with G. Pearlstein, Boundary components of Mumford-Tate domains, preprint, Duke Math. J. 165 (2016), 661-721. (pdf)
  34. with P. Griffiths and M. Green, Special values of automorphic cohomology classes, Mem. Amer. Math. Soc. 231 (2014), no. 1088, vi+145pp. (pdf)
  35. with C. Doran, J. Lewis and X. Chen, Normal functions, Picard-Fuchs equations, and elliptic fibrations on K3 surfaces, J. Reine Angew. Math. 721 (2016), 43-79. (pdf)
  36. with C. Doran, Algebraic K-theory of toric hypersurfaces, CNTP 5 (2011), no. 2, 397-600. (pdf) (publ. version)
  37. with P. Griffiths and M. Green, "Mumford-Tate groups and domains: their geometry and arithmetic", Annals of Math Studies, no. 183, Princeton University Press, 2012. (link)
  38. Shimura varieties: a Hodge-theoretic perspective, in "Hodge Theory (Cattani et al, Eds.)", Mathematical Notes 49, Princeton Univ. Press, Princeton, 2014, 525-566. (pdf)
  39. with X. Chen and J. Lewis, The sheaf of nonvanishing meromorphic functions in the projective algebraic case is not acyclic, C.R. Acad. Sci. Paris, Ser. I 348 (2010), 291-293 (pdf)
  40. with G. Pearlstein, Normal functions and the GHC, RIMS Kokyuroku 1745 (2011), 71-75. (pdf)
  41. with P. Griffiths and M. Green, Mumford-Tate domains, Bollettino dell' UMI (9) III (2010), 281-307. (pdf)
  42. with G. Pearlstein, An exponential history of functions with logarithmic growth, in "Topology of Stratified Spaces", MSRI Pub. 58, Cambridge University Press, New York, 2011.(pdf)
  43. with P. Griffiths and M. Green, Some enumerative global properties of variations of Hodge structure, Moscow Math. J. 9 (2009), 469-530.(pdf)
  44. with P. Griffiths and M. Green, Neron models and boundary components for degenerations of Hodge structures of mirror quintic type, in "Curves and Abelian Varieties (V. Alexeev, Ed.)", Contemp. Math 465 (2007), AMS, 71-145. (pdf)
  45. with P. Griffiths and M. Green, Neron models and limits of Abel-Jacobi mappings, Compositio Math. 146 (2010), 288-366.(pdf)
  46. with J. Lewis, The Abel-Jacobi map for higher Chow groups, II, Invent. Math 170 (2007), 355-420. (link)
  47. with J. Lewis and S. Mueller-Stach, The Abel-Jacobi map for higher Chow groups, Compositio Math. 142 (2006), no. 2, 374-396. (link)
  48. A survey of transcendental methods in the study of Chow groups of 0-cycles, in "Mirror Symmetry V" (Lewis, Yui and Yau, eds.), AMS/IP Stud. Adv. Math. 38 (2006), 295-350. (pdf)
  49. Exterior products of zero-cycles, J. reine. angew. Math. 142 (2006), 1-23. (link)
  50. Higher Abel-Jacobi maps for 0-cycles, J. K-Theory 2 (2008), 41-101. (link)
  51. A regulator formula for Milnor K-groups, K-Theory 29 (2003), 175-210. (pdf)
  52. An elementary proof of Suslin reciprocity, Canad. Math. Bull. 48 (2005), v. 2, 221-236. (pdf)
  53. "Geometric construction of regulator currents with applications to algebraic cycles", Princeton University Ph. D. Thesis, 2003. (ps)

Miscellany:

French singularity theory and a mathematical construction in Paris
Some musings on groupwork, blackboards, and plague
Eine mutige Lebensphilosophie und starke Pharma-Prioritaten in Bonn
Beilinson's beautiful essay on the spirit of mathematics
A guide if your complex functions get too complex
A bit of St. Louis in Venice
Abel-Jacobi graffiti in Durham
An intriguing interdisciplinary monograph in the Durham library
Durham cathedral
Today's weather forecast
Old undergraduate project ideas
Old Putnam practice notes