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:
- with R. Laza, Hodge theory of degenerations, (III): a vanishing cycle calculus for non-isolated singularities, preprint, 2023.
(link)
- with B. Castor, H. Deng and G. Pearlstein, Remarks on eigenspectra of isolated singularities, to appear in Pacific J. Math. (2024). (link)
- with C. Doran and S. Sinha Babu, K_{2} and quantum curves, to appear in ATMP (2024). (link)
- with P. Gallardo, Algebraic and analytic compactifications of moduli spaces, Notices of the AMS 69 (2022), no. 9, 1476-1485.
(publ. version)
(arXiv version)
- with V. Golyshev and T. Sasaki, Apéry extensions, J. London Math. Soc. 109 (2024), no. 1, e12825. (link)
- Unipotent extensions and differential equations (after Bloch-Vlasenko), CNTP 16 (2022), no. 4, 801-849. (link)
- with R. Laza, Hodge theory of degenerations, (II): vanishing cohomology and geometric applications, preprint, 2023.
(link)
- 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)
- with R. Laza and M. Saito, Smoothing of rational
singularities and Hodge structure, Algebraic Geometry 9 (2022), no. 4, 476-501.(link)
- 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)
- with M. Li, Two applications of the integral regulator,
Pacific J. Math. 306 (2020), 539-556. (link)
- Motivic irrationality proofs, preprint, 2020. (link)
- with G. Pearlstein and C. Robles, Polarized relations on
horizontal SL(2)s, Documenta Math. 24 (2019), 1179-1244. (link)
- 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)
- with Y. Yang, An explicit basis for the rational higher Chow
groups of abelian number fields, Ann. K-theory 3 (2018), 173-191. (link)
- Counting, sums, and series, preprint, 2018, to appear in
ASMI volume.
(pdf)
- with C. Robles, Variations of Hodge structure and orbits in
flag varieties, Adv. Math. 315 (2017), 27-87. (link)
- with S. Bloch and P. Vanhove, Local mirror symmetry and the
sunset Feynman integral, ATMP 21 (2017), 1373-1453. (link)
- with C. Robles, Classification of smooth horizontal Schubert
varieties, preprint, 2016, Euro. J. Math. 3 (2017), 289-310. (link)
- with R. Keast, Normal functions over locally symmetric
varieties, SIGMA 14 (2018), 116-133. (link)
- with J. Burgos Gil, J. Lewis and P. Lopatto, Simplicial Abel-Jacobi maps
and reciprocity laws, J. Alg. Geom. 27 (2018), 121-172. (link)
- 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)
- with S. Bloch and P. Vanhove, A Feynman integral via higher
normal functions, Compositio Math. 151 (2015), 2329-2375. (link)
- with I. Horozov, appendix to Reciprocity laws on
algebraic surfaces via iterated integrals, J. of
K-Theory 14 (2014), 304-310. (pdf)
- 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)
- with G. Pearlstein, Naive boundary strata and nilpotent
orbits, Ann. Inst. Fourier 64 (2014), 2659-2714. (pdf)
- with C. Doran, Algebraic cycles and local quantum
cohomology, CNTP 8 (2014), 703-727. (pdf)
- with P. Griffiths and M. Green, "Hodge Theory,
Complex Geometry and Representation Theory", CBMS Regional Conference Series in
Mathematics, Number 118, AMS, Providence, 2013.
- Cup products in automorphic cohomology: the case of
Sp_{4}, in "Hodge Theory, Complex Geometry,
and Representation Theory (Doran, Friedman, Nollet, Eds.)", Contemp. Math.
608, AMS, Providence, 2014, 199-234. (pdf)
- Notes on the representation theory of
SL_{2}(R), in "Hodge Theory, Complex Geometry,
and Representation Theory (Doran, Friedman, Nollet, Eds.)", Contemp. Math.
608, AMS, Providence, 2014, 173-198. (pdf)
- 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)
- Indecomposable K_{1} 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)
- with G. Pearlstein, Boundary components of Mumford-Tate
domains, preprint, Duke Math. J. 165 (2016), 661-721. (pdf)
- with P. Griffiths and M. Green, Special values of
automorphic cohomology classes, Mem. Amer. Math. Soc. 231 (2014), no.
1088, vi+145pp. (pdf)
- 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)
- with C. Doran, Algebraic K-theory of toric
hypersurfaces, CNTP 5 (2011), no. 2, 397-600. (pdf) (publ.
version)
- 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)
- Shimura varieties: a Hodge-theoretic perspective, in
"Hodge Theory (Cattani et al, Eds.)", Mathematical Notes 49, Princeton
Univ. Press, Princeton, 2014, 525-566. (pdf)
- 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)
- with G. Pearlstein, Normal functions and the
GHC, RIMS Kokyuroku 1745 (2011), 71-75. (pdf)
- with P. Griffiths and M. Green, Mumford-Tate domains,
Bollettino dell' UMI (9) III (2010), 281-307. (pdf)
- 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)
- with P. Griffiths and M. Green, Some enumerative global
properties of variations of Hodge structure, Moscow Math. J. 9
(2009), 469-530.(pdf)
- 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)
- with P. Griffiths and M. Green, Neron models and limits of
Abel-Jacobi mappings, Compositio Math. 146 (2010), 288-366.(pdf)
- with J. Lewis, The Abel-Jacobi map for higher Chow groups,
II,
Invent. Math 170 (2007), 355-420. (link)
- with J. Lewis and S. Mueller-Stach, The Abel-Jacobi map for
higher
Chow groups, Compositio Math. 142 (2006), no. 2, 374-396. (link)
- 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)
- Exterior products of zero-cycles, J. reine. angew. Math.
142 (2006), 1-23. (link)
- Higher Abel-Jacobi maps for 0-cycles, J.
K-Theory 2 (2008), 41-101. (link)
- A regulator formula for Milnor K-groups, K-Theory
29
(2003), 175-210. (pdf)
- An elementary proof of Suslin reciprocity, Canad. Math.
Bull.
48 (2005), v. 2, 221-236. (pdf)
- "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