# Matt Kerr

Cupples I, Room 114

office #: (314)-935-6746

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

**Recent and Upcoming Conferences:**

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

Intersection Homology
seminar

**Current Teaching:**

Number
Theory and Cryptography

**Some Course Notes:**

Matrix Algebra

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 July 2018

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: Tokio Sasaki; Soumya Sinha
Babu; Ben Castor

Ph.D. Graduates: Ryan
Keast (2016); Genival da
Silva Jr. (2016); Yu Yang (2017); Muxi Li (2018)

**Publications:**

**1.** with R. Laza, *Hodge theory of degenerations, (I):
consequences of the
decomposition theorem*, preprint, 2019. (link)

**2.** with M. Li, *Two applications of the integral regulator*,
preprint, 2018. (link)

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

**4.** *Motivic irrationality proofs*, preprint, 2017. (link)

**5.** with G. Pearlstein and C. Robles, *Polarized relations on
horizontal SL(2)s*, preprint, 2017. (link)

**6.** with P. del Angel, C. Doran, J. Iyer, J. Lewis, S.
Mueller-Stach, and D. Patel, *Specialization of cycles and the K-theory
elevator*, preprint, 2017. (link)

**7.** with Y. Yang, *An explicit basis for the rational higher Chow
groups of abelian number fields*, to appear in Annals of K-theory. (link)

**8.** with C. Robles, *Variations of Hodge structure and orbits in
flag varieties*, preprint, 2016, to appear in Adv. in Math. (link)

**9.** with S. Bloch and P. Vanhove, *Local mirror symmetry and the
sunset Feynman integral*, preprint, 2016, to appear in ATMP. (link)

**10.** with C. Robles, *Classification of smooth horizontal Schubert
varieties*, preprint, 2016, to appear in Euro. J. Math. (link)

**11.** with R. Keast, *Normal functions over locally symmetric
varieties*, preprint, 2015. (link)

**12.** with J. Lewis and P. Lopatto, *Simplicial Abel-Jacobi maps
and
reciprocity laws*, to appear in J. Alg. Geom. (link)

**13.** with G. da Silva Jr. and G. Pearlstein, *Arithmetic of
degenerating principal variations of Hodge
structure: examples arising from mirror symmetry and middle
convolution*, to appear in Canadian J. Math. (link)

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

**15.** with I. Horozov, appendix to *Reciprocity laws on
algebraic surfaces via iterated integrals*, to appear in J. of
K-Theory. (pdf)

**16.** *Algebraic and arithmetic properties of period maps*, to
appear in Fields Inst. Comm. (pdf)

**17.** with G. Pearlstein, *Naive boundary strata and nilpotent
orbits*, to appear in Annales de l'Institut Fourier. (pdf)

**18.** with C. Doran, *Algebraic cycles and local quantum
cohomology*, to appear in CNTP. (pdf)

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

**20.** *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)

**21.** *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)

**22.** 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)

**23.** *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)

**24.** with G. Pearlstein, *Boundary components of Mumford-Tate
domains*, preprint, to appear in Duke Math. J. (pdf)

**25.** with P. Griffiths and M. Green, *Special values of
automorphic cohomology classes*, to appear in Memoirs of the AMS. (pdf)

**26.** with C. Doran, J. Lewis and X. Chen, *Normal functions,
Picard-Fuchs equations, and elliptic fibrations on K3 surfaces*,
to appear in Crelle's Journal. (pdf)

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

**28.** 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)

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

**30.** 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)

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

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

**33.** 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)

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

**35.** 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)

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

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

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

**39.** *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)

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

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

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

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

**44.** "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