Matt Kerr

Cupples I, Room 114
office #: (314)-935-6746
e-mail: matkerr [at] math.wustl.edu

Recent and Upcoming Conferences:

I-70 Algebraic Geometry Symposium, November 2-3, 2019, St. Louis
(co-organized with R. Beheshti and M. Kumar)

PIMS Symposium on Hodge Theory, Arithmetic, and Moduli, May 13-17, 2019, Vancouver
(co-organized with C. Doran, M. Lalin, J. Lewis, and G. Pearlstein)

PIMS Postdoctoral Training School on Stochastic Dynamics and Hodge Theory, March 11-15, 2019, Edmonton
(co-organized with C. Doran and G. Pearlstein)

Link to old FRG website (incl. associated workshops)

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 Geometry seminar Instructions for Math Department Colloquium
D-module seminarGraduate Colloquium


Current Teaching:

Honors Mathematics I

Some Course Notes:

Linear Algebra
(Graduate) Complex Analysis II
(Graduate) Complex Analysis I
Algebraic cycles
Hodge Theory
(Graduate) Algebra I
Number Theory and Cryptography (book)
Undergraduate Algebraic Geometry (book) Washington University Math Circle

Research:

CV updated October 2019
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
Postdoctoral associates: Ivan Horozov (2011-2015); Patricio Gallardo (current)
Current Ph.D. Students: Soumya Sinha Babu; Ben Castor; Xiaojiang Cheng; Haohua Deng
Ph.D. Graduates: Ryan Keast (2016); Genival da Silva Jr. (2016); Yu Yang (2017); Muxi Li (2018), Tokio Sasaki (2019)

Publications:

1. with R. Laza and M. Saito, Smoothing of rational singularities and Hodge structure, preprint, 2019. (link)
2. with R. Laza, Hodge theory of degenerations, (I): consequences of the decomposition theorem, preprint, 2019. (link)
3. with M. Li, Two applications of the integral regulator, preprint, 2018. (link)
4. Counting, sums, and series, preprint, 2018, to appear in ASMI volume. (pdf)
5. Motivic irrationality proofs, preprint, 2017. (link)
6. with G. Pearlstein and C. Robles, Polarized relations on horizontal SL(2)s, Documenta Math. 24 (2019), 1179-1244. (link)
7. 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)
8. with Y. Yang, An explicit basis for the rational higher Chow groups of abelian number fields, Ann. K-theory 3 (2018), 173-191. (link)
9. with C. Robles, Variations of Hodge structure and orbits in flag varieties, Adv. Math. 315 (2017), 27-87. (link)
10. with S. Bloch and P. Vanhove, Local mirror symmetry and the sunset Feynman integral, ATMP 21 (2017), 1373-1453. (link)
11. with C. Robles, Classification of smooth horizontal Schubert varieties, preprint, 2016, Euro. J. Math. 3 (2017), 289-310. (link)
12. with R. Keast, Normal functions over locally symmetric varieties, SIGMA 14 (2018), 116-133. (link)
13. with J. Lewis and P. Lopatto, Simplicial Abel-Jacobi maps and reciprocity laws, J. Alg. Geom. 27 (2018), 121-172. (link)
14. 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)
15. with S. Bloch and P. Vanhove, A Feynman integral via higher normal functions, Compositio Math. 151 (2015), 2329-2375. (link)
16. with I. Horozov, appendix to Reciprocity laws on algebraic surfaces via iterated integrals, J. of K-Theory 14 (2014), 304-310. (pdf)
17. 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)
18. with G. Pearlstein, Naive boundary strata and nilpotent orbits, Ann. Inst. Fourier 64 (2014), 2659-2714. (pdf)
19. with C. Doran, Algebraic cycles and local quantum cohomology, CNTP 8 (2014), 703-727. (pdf)
20. with P. Griffiths and M. Green, "Hodge Theory, Complex Geometry and Representation Theory", CBMS Regional Conference Series in Mathematics, Number 118, AMS, Providence, 2013.
21. 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)
22. 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)
23. 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)
24. 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)
25. with G. Pearlstein, Boundary components of Mumford-Tate domains, preprint, Duke Math. J. 165 (2016), 661-721. (pdf)
26. with P. Griffiths and M. Green, Special values of automorphic cohomology classes, Mem. Amer. Math. Soc. 231 (2014), no. 1088, vi+145pp. (pdf)
27. 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)
28. with C. Doran, Algebraic K-theory of toric hypersurfaces, CNTP 5 (2011), no. 2, 397-600. (pdf) (publ. version)
29. 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)
30. Shimura varieties: a Hodge-theoretic perspective, in "Hodge Theory (Cattani et al, Eds.)", Mathematical Notes 49, Princeton Univ. Press, Princeton, 2014, 525-566. (pdf)
31. 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)
32. with G. Pearlstein, Normal functions and the GHC, RIMS Kokyuroku 1745 (2011), 71-75. (pdf)
33. with P. Griffiths and M. Green, Mumford-Tate domains, Bollettino dell' UMI (9) III (2010), 281-307. (pdf)
34. 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)
35. with P. Griffiths and M. Green, Some enumerative global properties of variations of Hodge structure, Moscow Math. J. 9 (2009), 469-530.(pdf)
36. 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)
37. with P. Griffiths and M. Green, Neron models and limits of Abel-Jacobi mappings, Compositio Math. 146 (2010), 288-366.(pdf)
38. with J. Lewis, The Abel-Jacobi map for higher Chow groups, II, Invent. Math 170 (2007), 355-420. (link)
39. with J. Lewis and S. Mueller-Stach, The Abel-Jacobi map for higher Chow groups, Compositio Math. 142 (2006), no. 2, 374-396. (link)
40. 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)
41. Exterior products of zero-cycles, J. reine. angew. Math. 142 (2006), 1-23. (link)
42. Higher Abel-Jacobi maps for 0-cycles, J. K-Theory 2 (2008), 41-101. (link)
43. A regulator formula for Milnor K-groups, K-Theory 29 (2003), 175-210. (pdf)
44. An elementary proof of Suslin reciprocity, Canad. Math. Bull. 48 (2005), v. 2, 221-236. (pdf)
45. "Geometric construction of regulator currents with applications to algebraic cycles", Princeton University Ph. D. Thesis, 2003. (ps)

Miscellany:

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
Undergraduate project ideas
Math Club talks on elliptic billiards, p-adics, and discrete Fourier transform
Old Putnam practice notes