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

 

Number Theory study group meets Sunday, 4pm Cupples I, room 202

 

Teaching previous years: (link)

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

 

 

Curriculum Vitae

 

Publication list

 

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:

2015 Non-commutative Hilbert modular symbols, (pdf), Algebra and Number Theory, Vol. 9 (2015), No. 2, 317–370 DOI: 10.2140/ant.2015.9.317

 

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.,  21(5):1111-1136. http://dx.doi.org/10.4310/MRL.2014.v21.n5.a9

 

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 (in high school) 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):

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

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

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

1993 (in high school) Tessellation of the four-dimensional space by regular polytopes, preprint, pdf

 

 

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).

 

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 (talk)

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

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

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

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

 

 

Personal:

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

My math-structure on TV: http://video.ketc.org/video/2365419242/

 

and in the WUSTL news: https://news.wustl.edu/news/Pages/four-dimensional-polytope.aspx

 

Links:

WUSTL Math Department

MIT news

MIT OpenCourseWare