Ivan Horozov

Ph.D., Mathematics, Brown University, 2004

B.A., Mathematics, MIT, 1998




Math 429 Linear Algebra (course info)

Classes – M, W, F – 12-1pm

Office hours: W 4-5pm, Th 2:30-3:30pm


Math 5031 Algebra I (course info)

Classes: Tu, Th 1-2:30pm

Office hours: W 4-5pm, Th 2:30-3:30pm


Teaching previous years: (link)

Ph.D. student: Zhenbin Luo, Ph.D. in Mathematics, Brandeis University, 2011


Curriculum Vitae




My research interests include mainly topics in Number Theory and Arithmetic Algebraic Geometry, more specifically, Cohomology of Arithmetic Groups, Modular Symbols, Multiple Dedekind Zeta Values, Reciprocity Laws on Algebraic Varieties. I was able to define a new type of higher dimentional iterated integrals, which I call iterated integrals over membranes, and I apply them extensively to define new modular symbols, reciprocity laws and analogues of multiple zeta values.

Published papers:

2014 Non-commutative Hilbert modular symbols, (pdf), Algebra and Number Theory, to appear


2014 Multiple Dedekind Zeta Functions, (pdf), Journal fuer die reine und angewandte Mathematik (Crelles Journal)}} DOI: 10.1515/crelle-2014-0055, July 2014


2014 Reciprocity Laws on Algebraic Surfaces via Iterated Integrals, with an appendix by Matt Kerr, (pdf), Journal of K-Theory, Volume  14 / Issue 02 / October 2014, pp 273 - 312 DOI: http://dx.doi.org/10.1017/is014006014jkt271


2014 Cohomology of GL(4,Z) with non-trivial coefficients, (pdf), accepted Math. Res. Lett., to appear


2013 (with Anton Deitmar), Iterated Integrals and higher order invariants, (pdf), Canad. J. Math. 65 (2013), 544-552 doi: 10.4153/CJM-2012-020-8,


2011 Non-abelian Reciprocity Laws on a Riemann Surface, Int. Math. Res. Notices (2011) (11): 2469-2495. doi: 10.1093/imrn/rnq160


2005 Euler characteristics of arithmetic groups, Math. Res. Lett., Volume 12, Issue 3, (2005) 275-291, doi: 10.4310/MRL.2005.v12.n3.a1


1993 Cubes in an integer lattice, Mathematics and Informatics, vol. 3, no 3, (1993) pp. 85-89



Submitted papers:

2014Multiple Zeta Values and Ideles, (pdf), submitted

2014 Double shuffle relations for multiple Dedekind zeta values (pdf) [math.NT], submitted


In preparation:

Parallel Transport on Higher Loop Spaces, preprint, (pdf), 2012

(with Zhenbin Luo), On the Contou-Carrere Symbol for Surfaces, arXiv:1310.7065, [math.AG], 2013

Book on iterated integrals (in preparation), 2013

Resourceful Preprints (not for publication):

A refinement of the Parshin symbol for surfaces, preprint, (pdf), (part of it submitted as Reciprocity Laws on Algebraic Surfaces via Iterated Integrals), 2010

Non-commutative two-dimensional modular symbol, preprint, (pdf), (part of it submitted as Non-commutative Hilbert modular symbols), 2006

Euler characteristics of arithmetic groups, thesis, (pdf), 94 pages, 2003, abbreviated version is already published

Tessellation of four-dimensional space by regular polytopes, preprint, 1994



Conference organizer:

Currently, I am organizing an AMS Special Session on Iterated integrals and its applications:

2015 Iterated integrals and applications, AMS Spring Northeastern Section Meeting, March 7-8, 2015, Georgetown, Washington, DC


2013 Modular forms, p-adic L-functions and Selmer groups July 7-13, 2013 - NIO (Oriahovitza), Bulgaria (co-organized with M. Dimitrov, J. Tilouine, E. Urban)


I am also organizing a

Number Theory Seminar: Fridays, Cupples I, Room 199; 4:30-6:00pm (schedule).



Summer School:

2014 June 30 - July 25, Clay Mathematics Institute Summer School, "Periods and Motives: Feynman amplitudes in the 21st century" ICMAT, 2014, Madrid, Spain, http://www.icmat.es/summerschool2014/


Talk presented at: Isaac Newton Institute for Mathematical Sciences, Cambridge, UK workshop: Grothendieck-Techmueller Theory and Multiple Zeta Values title: Multiple Dedekind Zeta Functions, April 2013 (with many questions by Don Zagier) (link to video)


Upcoming talks:

2014 September 20-21, AMS Sectional Meeting at the University of Wisconsin-Eau Claire, Eau Claire, WI

2014 October 25-26, AMS Sectional Meeting at San Francisco State University, San Francisco, CA

2014 November 8-9, AMS Sectional Meeting at the University of North Carolina, Greensboro, NC

2015 March 14-15, AMS Sectional meeting at Michigan State University, East Lansing, MI



Contact: Washington University in St. Louis, Department of Mathematics/ Cupples I, room 202

Phone: 314-935-8120

e-mail: horozov at math.wustl.edu





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