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. The Monodromy Conjecture for hyperplane arrangements (with N. Budur and Z. Teitler), available at arXiv:0906.1991.
2. Shokurov's ACC Conjecture for log canonical thresholds on smooth varieties (with T. de Fernex and L. Ein), to appear in Duke Math. J., available at arXiv:0905.3775.
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, J. Algebra 321 (2009), 128-151, available also at arXiv:0711.3794.
7. Limits of log canonical thresholds (with Tommaso de Fernex), Ann. Sci. Ecole. Norm. Sup. (4) 42 (2009), 491-515, available also at arXiv:0710.4978.

Teaching


Fall 2009. Math 631. Algebraic geometry I.
Winter 2009. Math 732. Toric varieties II.
Fall 2007. Math 631. Algebraic geometry I.
Winter 2007. I taught two sections of Math 412. Introduction to modern algebra.
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 will give a micicourse on "Invariants of singularities" at the IMPANGA Summer School in Algebraic Geometry, to be held between July 4-July 10, 2010 at Bedlowo, Poland.
2. I am one of the organizers of the MRC program in Commutative Algebra, to be held at Snowbird, Utah between June 26-July 2, 2010. The other organizers are David Eisenbud, Craig Huneke, and Claudia Polini.
3. I have coorganized with Lucia Caporaso, Brendan Hassett, James McKernan, and Mihnea Popa the introductory MSRI workshop Classical algebraic geometry today, between January 26-30, 2009. This was part of the MSRI program in algebraic geometry in Spring 2009.
4. Between July 7-25 I have coorganized with Jeff McNeal a program in Park City "Analytic and algebraic geometry: common problems-different methods".
5. 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.
6. 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.

Some events in Ann Arbor


1. Between May 17-22, 2010 we will have a conference on Frobenius splitting in algebraic geometry, commutative algebra, and representation theory .
2. During the week-end of November 14-15, 2008 we will have the Fall meeting of our OSU/UIC/UM algebraic geometry workshop.

Future and past conferences

1. A workshop on "Higher dimensional algebraic geometry", National Taiwan University in Taipei, March 29-April 2, 2010.
2. The conference "Classical and recent aspects in the study of projective varieties", University of Genova, January 21-22,2010.
3. Meeting on "Complex Algebraic Geometry" in Oberwolfach, September 28-October 2, 2009 in Oberwolfach.
4. Conference on Topology of Algebraic Varieties, in honor of Anatoly Libgober's 60th birthday, at Jaca, Spain, June 22-26, 2009.
5. The Combinatorial, Enumerative and Toric Geometry workshop at MSRI, March 23-27, 2009.
6. The workshop "On Resolution of Singularities", at RIMS, Kyoto University, December 1-5, 2008.
7. The workshop "Higher Dimensional Algebraic Geometry: Classification, Minimal Models, Fano Varieties and Stacks", Edinburgh, September 22-26,2008.
8. Park City program on "Analytic and algebraic geometry: common problems-different methods", July 7-25, 2008.

Photos

Here are some pictures taken while hiking in Utah.

mmustata@umich.edu