(Most recent version: http://math.mit.edu/~trasched/cv.html)
- US Citizenship
- Address: Department of Mathematics, Room 2-179; MIT; 77 Massachusetts
Cambridge, MA 02139
I am an AIM five-year fellow
and a C.L.E. Moore instructor in mathematics at MIT since Fall 2008.
- 2003-2008: University of Chicago: received Ph.D. under Victor Ginzburg.
- NSF Graduate Research Fellow
- Research Interests: Noncommutative Geometry, Representations of quivers and quantum groups.
- 2002-3: l'Ecole Normale Supérieure. Visiting foreign student.
- 1998-2002: Harvard University. Received B.A. summa cum laude in
- Wrote an undergraduate thesis "Troels Jorgensen's Once-Punctured Torus Theory" under Nathan Dunfield.
- Westinghouse STS Scholarship (5th place), Barry Goldwater Fellowship
Published and Posted Papers, with associated talks
- Normality and quadraticity for
special ample line bundles on toric varieties arising from root systems,
submitted (coauthored with Q. Gashi).
- Presented at AMS sectional meeting, combinatorial representation
theory session, Worcester, MA.
- Computational approaches to Poisson
traces associated to finite subgroups of Sp(2n,C), submitted (coauthored
with P. Etingof, S. Gong, A. Pacchiano, and Q. Ren).
- Presented at Inst. Henri Poincare and U. Manchester algebra
- Geometrization of principal
series representations of GL_N associated to regular characters
(coauthored with M. Kamgarpour).
- Presented at U. Toronto and U. Michigan geometry seminars.
- Curved infinity-algebras and
their characteristic classes , submitted (coauthored with A. Lazarev).
- On the asymptotic S_n-structure
of invariant differential operators on symplectic manifolds, submitted
(coauthored with Q. Ren).
- Presented at U. Paris 13 seminar
- Traces on finite W-algebras,
published in Transf. Groups.
- Looping of the numbers game and
the alcoved hypercube, accepted pending revisions to J. Combin. Theory
Ser. A (coauthored with Q. Gashi and D.
- Poisson traces and D-modules on
Poisson varieties, published in Geom. Funct. Anal. (coauthored with P. Etingof).
- Presented at Newcastle, Cambridge, MIT, Riverside AMS meetings,
and Boston University.
- On dominance and minuscule Weyl
group elements, published in J. Alg. Combin. (coauthored with Q. Gashi)
- Presented at U. Chicago seminar
- Zeroth Poisson homology of
symmetric powers of isolated quasihomogeneous surface singularities,
accepted to J. Reine und Angewandte Math. (coauthored with P. Etingof).
- Presented at Northeastern U. geometry seminar.
- Free products, cyclic homology,
and the Gauss-Manin connection, accepted (with revisions) to Advances in
Mathematics (coauthored with V. Ginzburg).
- Presented at Boston University seminar
- Superpotentials and higher
order derivations, published in J. Pure Appl. Algebra (coauthored with R. Bocklandt and M. Wemyss).
- Differential operators and BV
structures in noncommutative geometry", accepted to Selecta Math. (coauthored with V. Ginzburg).
- Presented at conferences at U. Leicester and U. Texas at Tyler, and
at seminar talks at U. Wisconsin, U. Antwerp, and
at U. Michigan
- Calabi-Yau Frobenius
algebras, published in J. Algebra (coauthored with C.-H. Eu).
- Presented at the
Banff Int. Res. Station's conference on Hochschild cohomology:
Structure and Applications, Sep 2007
- Presented at seminar talk at UC Riverside, Feb 28, 2008
- Hochschild homology of
preprojective algebras over the integers, accepted (with revisions) to
Advances in Mathematics.
- Presented at MIT, Antwerp, and Paris 7
- The necklace Lie
coalgebra and renormalization algebras, J. Noncommut. Geom. 2,
no. 2 (2008), 195--214 (coauthored with W. L. Gan).
- Presented by coauthor at AMS sectional meeting
- Twisted tensor
algebras, Yang-Baxter equations, twists for Hopf algebras, and double
Poisson algebras, revised and expanded version accepted to Contemp. Math.
- Moyal quantization
and stable homology of necklace Lie algebras, Mosc. Math. J. 6, no. 3 (2006), 431--459 (coauthored with V. Ginzburg).
- A Hopf algebra
quantizing a necklace Lie algebra canonically associated to a quiver,
Int. Math. Res. Not. 12 (2005), 725--760.
- Presented at the joint AMS-SIAM conference, summer 2004, and at
seminar talks at MIT and Yale
Trigonometric solutions of the associative Yang-Baxter equation,
Math. Res. Lett. 10 (2003), 301-321.
- Presented at the Ecole Polytechnique for
the quantum groups seminar, 2003
Proof of the GGS Conjecture,
Math. Res. Lett. 7 (2000), no.5-6, 801-826.
quantization of dynamical r-matrices for finite dimensional semisimple
Lie algebras, J. Amer. Math. Soc., 13 (2000), no. 3, 595-609 (co-authored with P. Etingof and O. Schiffmann).
- Presented at the workshop on Deformations and Quantization at Northeastern University, 1999
- Set-theoretical solutions
to the quantum Yang-Baxter equation, Duke Math. J., 100 (1999), no. 2, 169-209 (co-authored with P. Etingof and A. Soloviev).
- Presented at Loyola University, 1999
- Advances in Mathematics, International Mathematics Research Notices, Manin Festschrift, Journal of Algebra, European Journal of Combinatorics.
Teaching and related experience
- Fall 2010: Linear algebra at MIT (18.700), Instructor
- Fall 2008: Topics course in algebra on quiver representations at MIT
- 2007-2008: Math Methods for Soc. Sci. at U. Chicago (Math 195--6),
- 2005-2006: Calculus at U. Chicago (Math 151--3), Instructor
- 2004-2005: College Fellow for Math 270 (Complex Analysis) and Math
203--4 (Analysis) at U. Chicago.
- January 2005: Planned and taught a week-long, 15 hour course at the Illinois Mathematics and Science Academy on topology, geometry, and trigonometry of surfaces, together with Matt Day.
- Mentor for Bill Chen, whose combinatorics project
placed in the semifinals of the Intel Science Talent Search.
- 2003-2006: Tutor and student director of the University of Chicago Community Service Center's "Absolute Value Math Camp", an intense quarterly two-week, 20 hour tutoring program for area middle schools
- Won the President's Volunteer Service award, an annual award given by the University of Chicago to two students to recognize service
- 2002-3: Completed first year of the third cycle of organ interpretation at the 5th district Conservatory of Paris, mentionné bien
- Summer 2001: volunteer overnight supervisor, van driver, and computer technician for the St. James Summer Homeless Shelter run by Harvard students.