Ilya Shapiro

Assistant Professor
Department of Mathematics and Statistics
University of Windsor

Contact Information

Office: 

  Lambton Tower (LT) Room 10-113

Phone: 

  (519) 253-3000 ext. 4734

Email: 

  ishapiro at uwindsor dot ca

Research

I am interested in representations of affine Kac-Moody Lie algebras coming from D-modules, various orbifold invariants, Frobenius actions on cohomology, and groups with symplectic self-duality.

Curriculum Vitae

My CV in pdf format.

Publications

Frobenius map and the $p$-adic Gamma function, Journal of Number Theory, Volume 132, Issue 8, 1770-1779,  arXiv:1006.0382.

Locally compact abelian groups with symplectic self-duality (with A. Prasad, M. K. Vemuri), Advances in Mathematics 225 (2010), no. 5, 2429-2454, arXiv:0906.4397.

Frobenius map for quintic threefolds, International Mathematics Research Notices (2009), Volume 2009, Number 13, 2519-2545, arXiv:0809.3742.

Frobenius map on local Calabi-Yau manifolds, Journal of Mathematical Physics 50 (2009), no. 2, 022302, 14 pp., arXiv:0810.2195.

The BRST reduction of the chiral Hecke algebra, Advances in Mathematics 220 (2009), no. 6, 1657-1688, math.RT/0609770.

Twisted de Rham cohomology, homological definition of the integral and "Physics over a ring" (with A. Schwarz), Nuclear Physics B, Volume 809 (3), p.547-560,  arXiv:0809.0086.

$p$-adic superspaces and Frobenius (with A. Schwarz), Communications in Mathematical Physics, Volume 282, Number 1, p. 87-113, 2008, math.NT/0605310.

Gelfand-Fuchs cohomology of invariant formal vector fields (with X. Tang), Mathematical Research Letters, Volume 15, Number 1, p. 129-149, math.RT/0607582.

Supergeometry and Arithmetic Geometry (with A. Schwarz), Nuclear Physics B, Volume 756, Issue 3, p. 207-218, hep-th/0605119.

Some remarks on Gopakumar-Vafa invariants (with A. Schwarz), Pure and Applied Mathematics Quarterly, Vol 1, Number 4, p. 817-826, 2005, hep-th/0412119.

Public author identifier: http://arxiv.org/a/shapiro_i_1.

Teaching

University of Windsor (Winter 2011-present).  Fully responsible for all instruction.

- 62-120 Linear Algebra.
- 62-126 Linear Algebra (Engineering).
- 62-322 Number Theory.

University of Waterloo (Fall 2010).  Fully responsible for all instruction.  Grading assisted by Graduate Teaching Assistants.  Lab component handled by the Engineering department.

- MATH 211 Advanced Calculus (Electrical and Computer Engineering).

University of California at Davis (2004-2007).  Fully responsible for all instruction. Grading assisted by Readers and Teaching Assistants.  Class sizes from 20 to 240 students.  Teaching load of 3 to 4 quarter length courses per year.

- MAT-016A/B Short Calculus.

- MAT-021A/B Calculus.

- MAT-115B Number Theory.

- MAT-167 Applied Linear Algebra.

- MAT-150B Modern Algebra.

University of Chicago (2000-2004).  Fully responsible for all instruction. Grading assisted by Teaching Assistant.  Class sizes from 10 to 30 students.  Teaching load of 3 quarter length courses per year.

- Math 151-152-153 Calculus.

- Math 195-196 Multi-variable Calculus and Linear Algebra.

Personal

Married to Barbara Csima.