Mircea Mustaţă

I am an Associate 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. Bernstein-Sato polynomials in positive characteristic, available at arXiv:0711.3794.
2. Limits of log canonical thresholds (with Tommaso de Fernex), available at arXiv:0710.4978.
3. Generically finite morphisms and formal neighborhoods of arcs (with Lawrence Ein), available at arXiv:0708.3880.
4. F-thresholds, tight closure, integral closure, and multiplicity bounds (with Craig Huneke, Shunsuke Takagi, and Kei-ichi Watanabe), available at arXiv:0708.2394.
5. Test ideals vs. multiplier ideals (with Ken-ichi Yoshida), available at arXiv:0706.1124.
6. F-thresholds of hypersurfaces (with Manuel Blickle and Karen Smith), available at arXiv:0705.1210.
7. Jet schemes and singularities (with Lawrence Ein), available at math.AG/0612862.
8. Discreteness and rationality of F-thresholds (with Manuel Blickle and Karen Smith), available at math/0607660.
9. Restricted volumes and base loci of linear series (with Lawrence Ein, Rob Lazarsfeld, Michael Nakamaye, and Mihnea Popa), available at math.AG/0607221.
10. Invariants of singularities (with Lawrence Ein), International Congress of Mathematicians, Vol. II, 583--602, Eur. Math. Soc., Zurich, 2006, available also at math.AG/0604601.

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 Jeff McNeal a program in Park City between July 7-25, 2008. The title of the program is "Analytic and algebraic geometry: common problems-different methods".
2. 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.
3. 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.
4. 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 March 4-7, 2008 we had the fourth Spring Lectures in Algebraic Geometry. The lecturer was Ravi Vakil.
2. Between August 6-10, 2007 we had a workshop on F-singularities and D-modules. I hope that at some point I will get to scan my notes and make them available.

Future and past conferences

1. The workshop "On Resolution of Singularities", at RIMS, Kyoto University, December 1-5, 2008.
2. The workshop "Higher Dimensional Algebraic Geometry: Classification, Minimal Models, Fano Varieties and Stacks", Edinburgh, September 22-26,2008.
3. Park City program on "Analytic and algebraic geometry: common problems-different methods", July 7-25, 2008.
4. The conference "Commutative Algebra and its Interaction with Algebraic Geometry" at Banff, June 10-15, 2007.
5. The conference Advances in algebra and geometry, at MSRI, Berkeley, in honor of David Eisenbud, April 28-May 05, 2007.
6. A workshop on "Minimal and canonical models in algebraic geometry" at MSRI, Berkeley, April 16-20, 2007.

mmustata@umich.edu