Mircea Mustaţă

I am a Professor in the Department of Mathematics at University of Michigan. I am supported by the NSF and by a Packard Fellowship. Here is my contact information.

My work is in algebraic geometry. In the last couple of years my main interest was in various invariants of singularities of algebraic varieties, such as minimal log discrepancies, log canonical thresholds, multiplier ideals, Bernstein-Sato polynomials or F-thresholds. Various points of view and techniques come in the picture when studying these invariants: resolutions of singularities, jet schemes, D-modules or positive characteristic methods. Other interests include birational geometry, asymptotic base loci and invariants of divisors, and toric varieties.

Here are my CV and a list of publications.

Papers

You can find here my papers on the archive. Here are a few recent ones:

1. Log canonical thresholds on smooth varieties: the Ascending Chain Condition (with L. Ein), available at arXiv:0811.4444.
2. The Ascending Chain Condition for log canonical thresholds on l.c.i. varieties (with T. de Fernex), available at arXiv:0811.4642.
3. Toward an inductive description of singularities of pairs, available at arXiv:0809.2352 .
4. Convex bodies associated to linear series (with R. Lazarsfeld), to appear in Ann. Sci. Ecole Norm. Sup., available at arXiv:0805.4559.
5. Positivity for toric vector bundles (with M. Hering and S. Payne), to appear in Ann. Inst. Fourier (Grenoble), available at arXiv:0805.4035.
6. Bernstein-Sato polynomials in positive characteristic, to appear in J. Algebra, available at arXiv:0711.3794.
7. Limits of log canonical thresholds (with Tommaso de Fernex), to appear in Ann. Sci. Ecole. Norm. Sup., available at arXiv:0710.4978.

Teaching


Fall 2007. Math 631. Algebraic geometry I.
Winter 2007. I taught two sections of Math 412. Introduction to modern algebra.
Fall 2006. I was on leave at IAS, Princeton.
Winter 2006. Math 632. Algebraic geometry II (Schemes and cohomology). You can find here the homework assignments and the problems covered in the discussion session.
Fall 2005. Math 615. Advanced topics in Algebra (Introduction to D-modules).
Fall 2004, Winter 2005. Math 731 and 732. Topics in Algebraic Geometry I and II (Toric varieties).

Toric varieties


Here are lecture notes for the course I taught on toric varieties. Some chapters are just expanded versions of the corresponding chapters in Bill Fulton's book "Introduction to toric varieties", using also Bill's lecture notes for a course he taught a few years ago. Some chapters are still missing, but hopefully they will be available soon (in particular, there will be chapters on homogeneous coordinate rings and toric variations of GIT quotients, nondegenerate hypersurfaces with respect to their Newton polyhedra and toric mirror symmetry, after Batyrev and Borisov).

Other activities

1. I am coorganizing with Lucia Caporaso, Brendan Hassett, James McKernan, and Mihnea Popa the introductory MSRI workshop Classical algebraic geometry today, to be held between January 26-30, 2009. This is part of the MSRI program in algebraic geometry in Spring 2009.
2. Between July 7-25 I have coorganized with Jeff McNeal a program in Park City "Analytic and algebraic geometry: common problems-different methods".
3. In December 2007 the Clay Mathematics Institute organized the Clay Lectures at the Tata Institute, in Mumbai. I was one of the lecturers, the other one being Elon Lindenstrauss.
4. In August 2006 Stefan Kebekus and Thomas Eckl organized a Summerschool in Cologne on "Moduli spaces and arcs in birational geometry". I was one of the lecturers and working group mentors (the other two were Gabi Farkas and Mihnea Popa). Here are my lecture notes.
5. I have coorganized with Nero Budur, Lawrence Ein, Rob Lazarsfeld and Vyacheslav V. Shokurov an AIM workshop on "Numerical invariants of singularities and higher-dimensional algebraic varieties" in Palo Alto, in June 2006.

Some events in Ann Arbor


1. Between May 4-8, 2009 we will have a Workshop on Fourier-Mukai functors, regularity on abelian varieties, and Generic Vanishing theorems. The two lecturers will be Giuseppe Pareschi and Mihnea Popa.
2. During the week-end of October 18-19, 2008 we had the Fall meeting of our OSU/UIC/UM algebraic geometry workshop.
3. Between July 31st-August 5th, 2008 we had a commutative algebra conference , to celebrate Mel Hochster's 65th birthday.
4. Between August 6-10, 2007 we had a workshop on F-singularities and D-modules.

Future and past conferences

1. Special session on Commutative Algebra at the PRIMA congress in Sydney, Australia, July 6-10, 2009.
2. Conference on Topology of Algebraic Varieties, in honor of Anatoly Libgober's 60th birthday, at Jaca, Spain, June 22-26, 2009.
3. The Combinatorial, Enumerative and Toric Geometry workshop at MSRI, March 23-27, 2009.
4. The workshop "On Resolution of Singularities", at RIMS, Kyoto University, December 1-5, 2008.
5. The workshop "Higher Dimensional Algebraic Geometry: Classification, Minimal Models, Fano Varieties and Stacks", Edinburgh, September 22-26,2008.
6. Park City program on "Analytic and algebraic geometry: common problems-different methods", July 7-25, 2008.
7. The conference "Commutative Algebra and its Interaction with Algebraic Geometry" at Banff, June 10-15, 2007.
8. The conference Advances in algebra and geometry, at MSRI, Berkeley, in honor of David Eisenbud, April 28-May 05, 2007.
9. A workshop on "Minimal and canonical models in algebraic geometry" at MSRI, Berkeley, April 16-20, 2007.

Photos

Here are some pictures taken while hiking in Utah.

mmustata@umich.edu