**Ivan Horozov**

Ph.D., Mathematics, Brown University, 2004

B.A., Mathematics, MIT, 1998

**Teaching Spring 2015:**

Math 310 Foundations for Higher Mathematics (course info)

Classes: M, W, F – 1-2pm

Office hours: Wed 4-5pm, Fri 11am -12pm, or by appointment

Math 5032 Algebra II (course info)

Classes: M, W, F
– 3-4pm

Office hours: Wed 4-5pm, Fri 11am -12pm, or by
appointment

Teaching previous years: (link)

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

**Research:**

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:*

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

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

*In preparation:*

Multiple Dedekind Zeta Values and Adeles 2015

Zeta Function of varieties and double
shuffle 2015

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

Book on iterated
integrals **( in
preparation), **2013

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

*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

Abstracts deadline:

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).

**Recent scholarships: **

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)

**Recent and upcoming talks:**

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

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

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

2015 February 5^{th}, Colloquium
talk at the University of New Mexico, Albuquerque, NM
(abstract)

2015 March 7-8, 2015,
Georgetown, Washington, DC (abstract)

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

**Contact info:** Washington
University in St. Louis,

Department of
Mathematics/ Cupples I, room 202

Phone: 314-935-8120

e-mail: horozov at math.wustl.edu

MathArt:
http://www.math.wustl.edu/News2015/News2015_Jan_Polytope.html

Links: