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 past few 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 and 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. Estimates for F-jumping numbers and bounds for Hartshorne-Speiser-Lyubeznik numbers (with Wenliang Zhang), available at arXiv:1110:5687.
2. The non-nef locus in positive characteristic, available at arXiv:1109.3825.
3. IMPANGA lecture notes on log canonical thresholds, available at arXiv:1107.2676.
4. Multiplier ideals via Mather discrepancy (with Lawrence Ein and Shihoko Ishii), available at arXiv:1107.2192.
5. Log canonical thresholds, F-pure thresholds, and non-standard extensions (with Bhargav Bhatt, Daniel Hernandez, and Lance Miller), available at arXiv:1106.0207.
6. Ordinary varieties and the comparison between multiplier ideals and test ideals II, available at arXiv:1012.2915.
7. Ordinary varieties and the comparison between multiplier ideals and test ideals (with V. Srinivas), available at arXiv:1012.2818.
8. A finiteness property of graded sequences of ideals (with M. Jonsson), available at arXiv:1011.3967.
9. Valuations and asymptotic invariants of sequences of ideals (with M. Jonsson), available at arXiv:1011.3699.

Teaching


Winter 2011. Math 732. Zeta functions in algebraic geometry. Here are the lecture notes from the course.
Winter 2010. Math 632. Algebraic geometry II.
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. Nero Budur, Francois Loeser, and I will organize a thematic program Motivic invariants and singularities at Notre Dame, between May 20-June 7, 2013.
2. Craig Huneke, Yujiro Kawamata, Karen Smith, Kei-ichi Watanabe, and I are organizing the workshop The Commutative Algebra of Singularities in Birational Geometry: Multiplier Ideals, Jets, Valuations, and Positive Characteristic Methods at MSRI, between May 6-10, 2013, as part of the Commutative Algebra program in 2012-2013.
3. I gave a micicourse on "Invariants of singularities" at the IMPANGA Summer School in Algebraic Geometry, held between July 4-10, 2010 at Bedlowo, Poland. Here are the lecture notes.
4. David Eisenbud, Craig Huneka, Claudia Polini, and I were the mentors of the MRC program in Commutative Algebra, held at Snowbird, Utah between June 26-July 2, 2010. The other organizers were David Eisenbud, Craig Huneke, and Claudia Polini.
5. Lucia Caporaso, Brendan Hassett, James McKernan, Mihnea Popa, and I have organized 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.
6. Jeff McNeal and I organized a program in Park City "Analytic and algebraic geometry: common problems-different methods", between July 7-25, 2008.
7. 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 April 3-6, 2012 Bjorn Poonen will give a series of lectures, as part of our Spring Lectures in Algebraic Geometry.
2. Between May 16-19, 2013 we will have an algebraic geometry conference in honor of Rob Lazarsfeld's 60th birthday.

Future and past conferences

1. The conference Characterictic p and p-adic geometry, at Johannes Gutenberg University, Mainz, June 4-8, 2012.
2. The AIM workshop ACC for minimal log discrepancies and termination of flips, May 14-18, 2012.
3. Algebraic geometry conference, Bangkok, December 19-23, 2011.
4. A conference in Luminy, in September 2011, in honour of Jan Denef's 60th birthday.
5. AIM workshop Relating test ideals and multiplier ideals, August 8-12, 2011.
6. The conference "Minimal models and extremal rays", Kyoto, June 20-24, 2011, on the occasion of the 60th birthday of Shigefumi Mori.
7. The conference "Birational geometry", Edinburgh, December 6-10, 2010, in honour of Slava Shokurov's 60th birthday.

Photos

Here are some pictures taken while hiking in Utah.

mmustata@umich.edu