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

1. Weight functions on non-archimedean analytic spaces and the Kontsevich-Soibelman skeleton (with Johannes Nicaise), available at arXiv:1212.6328.

2. On the numerical dimension of pseudo-effective divisors in positive characteristic (with Paolo Cascini, Christopher Hacon, and Karl Schwede), available at arXiv:1206.6521.

3. An algebraic approach to the openness conjecture of Demailly and Kollar (with Mattias Jonsson), available at arXiv:1205.4273.

4. A Frobenius variant of Seshadri constants (with Karl Schwede), available at arXiv:1203.1081.

5. The augmented base locus in positive characteristic (with Paolo Cascini and James McKernan), available at arXiv:1111.3236.

6. The non-nef locus in positive characteristic, available at arXiv:1109.3825.

Here are some resources for the courses that I recently taught.

Fall 2013. Math 731. Spaces of arcs and singularities in birational geometry. The lecture notes for this class are becoming the last chapters in this book that Tommaso de Fernex, Lawrence Ein, and I are currently writing.

Winter 2013. Math 732. Introduction to birational geometry. The lecture notes for this class have become part of the first four chapters in the book linked above.

Winter 2012. Math 732. Introduction to diophantine approximation on abelian varieties. Mitya Boyarchenko kindly posted scanned versions of his notes here.

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.

Fall 2007. Math 631. Algebraic geometry I.

Winter 2006. Math 632. Algebraic geometry II (Schemes and cohomology). Here are the homework assignments and the problems covered in the discussion session.

Fall 2004, Winter 2005. Math 731 and 732. Topics in Algebraic Geometry I and II (Toric varieties). Here are the lecture notes, though some chapters are still missing. The first 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.

2. Claude Sabbah, Christian Schnell, and I organized a workshop on Saito's theory of mixed Hodge modules, at the Clay Mathematics Institute, in Oxford (UK), between August 19-23, 2013.

3. Marian Aprodu, Mihnea Popa, and I organized a special session on algebraic geometry at the Joint International Meeting of the AMS and the Romanian Mathematical Society, in Alba Iulia (Romania), between June 27-30, 2013.

4. Nero Budur, Francois Loeser, and I organized a thematic program Motivic invariants and singularities at Notre Dame, between May 20-June 7, 2013.

5. Christopher Hacon, Mihnea Popa, and I organized an algebraic geometry conference between May 16-19, 2013, in Ann Arbor, in honor of Rob Lazarsfeld's 60th birthday.

6. Craig Huneke, Yujiro Kawamata, Karen Smith, Kei-ichi Watanabe, and I organized 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.

7. 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.

8. David Eisenbud, Craig Huneke, Claudia Polini, and I were the mentors of the MRC program in Commutative Algebra, held at Snowbird, Utah between June 26-July 2, 2010.

9. Lucia Caporaso, Brendan Hassett, James McKernan, Mihnea Popa, and I 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.

10. Jeff McNeal and I organized a program in Park City "Analytic and algebraic geometry: common problems-different methods", between July 7-25, 2008.

11. 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.

1. Between May 26-June 22, 2014 we will have a special month dedicated to birational geometry in zero and positive characteristics.

2. Between April 15-17, 2014, Manjul Bhargava will give a series of lectures, as part of our Spring Lectures in Algebraic Geometry.

2. The “Classical algebraic geometry” workshop, Oberwolfach, June 30-July 4, 2014.

3. The workshop “Birational geometry and foliations”, Bonn, February 24-28, 2014.

4. The conference Géométrie birationnelle des variétés algébriques complexes, in honor of Frederic Campana's 60th birthday, Luminy, October 7-11, 2013.

5. Conference on Complex geometry at the Institute for Mathematical Sciences, Singapore, July 26-August 5, 2013.

6. The AIM workshop The minimal model program in characteristic p, April 29-May 3, 2013.