# Matt Kerr

Cupples I, Room 114

e-mail: matkerr [at] math.wustl.edu

**Recent and Upcoming Conferences:**

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

Étale cohomology
reading seminar
Washington University Math Circle

**Current Teaching (Spring 2023):**

Linear Algebra

(Graduate) Complex Analysis II

**Some Course Notes:**

Matrix Algebra

Algebraic Geometry

Calculus of Several Variables

(Graduate) Algebra II

(Graduate) Algebra I

Hodge Theory

Algebraic cycles
Number Theory and Cryptography (book)

**Research:**

CV updated October 2022

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)

Current Ph.D. Students:
Xiaojiang Cheng;
RJ Acuna;
Devin Akman

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 B. Castor, H. Deng and G. Pearlstein, *Remarks on eigenspectra of isolated singularities*, preprint, 2022. (link)

**2.** with C. Doran and S. Sinha Babu, *K*_{2} and quantum curves, preprint, 2021. (link)

**3.** with P. Gallardo, *Algebraic and analytic compactifications of moduli spaces*, Notices of the AMS 69 (2022), no. 9, 1476-1485.
(publ. version)
(arXiv version)

**4.** with V. Golyshev and T. Sasaki, *Apéry extensions*, preprint, 2020. (link)

**5.** *Unipotent extensions and differential equations (after Bloch-Vlasenko)*, CNTP 16 (2022), no. 4, 801-849. (link)

**6.** with R. Laza, *Hodge theory of degenerations, (II): vanishing
cohomology and geometric applications*, preprint, 2020.
(link)

**7.** with P. Gallardo and L. Schaffler, *Geometric interpretation of
toroidal compactifications of moduli of points in the line and cubic surfaces*,
to appear in Adv. Math. (link)

**8.** with R. Laza and M. Saito, *Smoothing of rational
singularities and Hodge structure*, to appear in Algebraic Geometry. (link)

**9.** with R. Laza, *Hodge theory of degenerations, (I):
consequences of the
decomposition theorem*, to appear in Selecta Math. (link)

**10.** with M. Li, *Two applications of the integral regulator*,
preprint, to appear in Pacific J. Math. (link)

**11.** *Counting, sums, and series*, preprint, 2018, to appear in
ASMI volume.
(pdf)

**12.** *Motivic irrationality proofs*, preprint, 2017. (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.** with C. Robles, *Variations of Hodge structure and orbits in
flag varieties*, Adv. Math. 315 (2017), 27-87. (link)

**17.** with S. Bloch and P. Vanhove, *Local mirror symmetry and the
sunset Feynman integral*, ATMP 21 (2017), 1373-1453. (link)

**18.** with C. Robles, *Classification of smooth horizontal Schubert
varieties*, preprint, 2016, Euro. J. Math. 3 (2017), 289-310. (link)

**19.** with R. Keast, *Normal functions over locally symmetric
varieties*, SIGMA 14 (2018), 116-133. (link)

**20.** with J. Lewis and P. Lopatto, *Simplicial Abel-Jacobi maps
and
reciprocity laws*, J. Alg. Geom. 27 (2018), 121-172. (link)

**21.** 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)

**22.** with S. Bloch and P. Vanhove, *A Feynman integral via higher
normal functions*, Compositio Math. 151 (2015), 2329-2375. (link)

**23.** with I. Horozov, appendix to *Reciprocity laws on
algebraic surfaces via iterated integrals*, J. of
K-Theory 14 (2014), 304-310. (pdf)

**24.** *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)

**25.** with G. Pearlstein, *Naive boundary strata and nilpotent
orbits*, Ann. Inst. Fourier 64 (2014), 2659-2714. (pdf)

**26.** with C. Doran, *Algebraic cycles and local quantum
cohomology*, CNTP 8 (2014), 703-727. (pdf)

**27.** with P. Griffiths and M. Green, "Hodge Theory,
Complex Geometry and Representation Theory", CBMS Regional Conference Series in
Mathematics, Number 118, AMS, Providence, 2013.

**28.** *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)

**29.** *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)

**30.** 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)

**31.** *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)

**32.** with G. Pearlstein, *Boundary components of Mumford-Tate
domains*, preprint, Duke Math. J. 165 (2016), 661-721. (pdf)

**33.** with P. Griffiths and M. Green, *Special values of
automorphic cohomology classes*, Mem. Amer. Math. Soc. 231 (2014), no.
1088, vi+145pp. (pdf)

**34.** 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)

**35.** with C. Doran, *Algebraic *K*-theory of toric
hypersurfaces*, CNTP **5** (2011), no. 2, 397-600. (pdf) (publ.
version)

**36.** 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)

**37.** *Shimura varieties: a Hodge-theoretic perspective*, in
"Hodge Theory (Cattani et al, Eds.)", Mathematical Notes 49, Princeton
Univ. Press, Princeton, 2014, 525-566. (pdf)

**38.** 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)

**39.** with G. Pearlstein, *Normal functions and the
GHC*, RIMS Kokyuroku **1745** (2011), 71-75. (pdf)

**40.** with P. Griffiths and M. Green, *Mumford-Tate domains*,
Bollettino dell' UMI (9) **III** (2010), 281-307. (pdf)

**41.** 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)

**42.** with P. Griffiths and M. Green, *Some enumerative global
properties of variations of Hodge structure*, Moscow Math. J. **9**
(2009), 469-530.(pdf)

**43.** 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)

**44.** with P. Griffiths and M. Green, *Neron models and limits of
Abel-Jacobi mappings*, Compositio Math. **146** (2010), 288-366.(pdf)

**45.** with J. Lewis, *The Abel-Jacobi map for higher Chow groups,
II*,
Invent. Math **170** (2007), 355-420. (link)

**46.** with J. Lewis and S. Mueller-Stach, *The Abel-Jacobi map for
higher
Chow groups*, Compositio Math. **142** (2006), no. 2, 374-396. (link)

**47.** *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)

**48.** *Exterior products of zero-cycles*, J. reine. angew. Math.
**142** (2006), 1-23. (link)

**49.** *Higher Abel-Jacobi maps for 0-cycles*, J.
K-Theory **2** (2008), 41-101. (link)

**50.** *A regulator formula for Milnor K-groups*, K-Theory
**29**
(2003), 175-210. (pdf)

**51.** *An elementary proof of Suslin reciprocity*, Canad. Math.
Bull.
**48** (2005), v. 2, 221-236. (pdf)

**52.** "Geometric construction of regulator currents with applications
to
algebraic cycles", Princeton University Ph. D. Thesis, 2003.
(ps)

**Miscellany:**

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