I am a Professor in the
Department of Mathematics
at University of Michigan.
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. Local vanishing and Hodge filtration for rational singularities (with Sebastián Olano and Mihnea Popa), available at arXiv:1703.06704.

2. Restriction, subadditivity, and semicontinuity theorems for Hodge ideals (with Mihnea Popa), available at arXiv:1606.05659.

3. Hodge ideals (with Mihnea Popa), available at arXiv:1605.08088.

4. The volume of a set of arcs on a variety (with Tommaso de Fernex), available at arXiv:1506.06424.

5. A boundedness conjecture for minimal log discrepancies on a fixed germ (with Yusuke Nakamura), available at arXiv:1502.00837.

6. The combinatorics and topology of proper toric maps (with Mark de Cataldo and Luca Migliorini), available at arXiv:1407.3497.

7. The dimension of jet schemes of singular varieties, available at arXiv:1404.7731.

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

Fall 2017. Math 631. Algebraic geometry I.

Winter 2017. Math 732. Rationality of algebraic varieties. Here are some notes that Takumi Murayama Live TeX-ed during lectures. For most of the course I also posted lecture notes here.

Fall 2016. Math 593. Algebra I.

Fall 2015. Math 565. Combinatorics and graph theory and Math. 412. Introduction to modern algebra.

Winter 2015. Math 412. Introduction to modern algebra.

Fall 2014. Math 711. Topics in birational geometry.

Winter 2014. Math 537. Introduction to differential topology.

Fall 2013. Math 731. Spaces of arcs and singularities in birational geometry.

Winter 2013. Math 732. Introduction to birational geometry.

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. Daniel Erman, Claudiu Raicu, Greg Smith, and I are organizing the conference “A view towards algebraic geometry“, on the occasion of David Eisenbud's 70th birthday. This will be held at the Harbor View Hotel on Martha’s Vineyard, between May 1-5, 2017.

3. Tommaso de Fernex, Karl Schwede, and I organized the Summer school and conference Higher dimensional algebraic geometry, held at the University of Utah, July 18-26, 2016.

4. Tommaso de Fernex, Brendan Hassett, Martin Olsson, Mihnea Popa, Richard Thomas, and I organized a successor to Seattle 2005 (and Santa Cruz 1995, Bowdoin 1985, Arcata 1974, Woods Hole 1964). This happended between July 13-31, 2015, at the University of Utah.

1. In Winter 2017 we will have a new edition of the Spring Lectures in Algebraic Geometry. The speakers will be Zhiwei Yun.

2. Conference in Complex Analysis and Geometry in honor of Jean-Pierre Demailly, Grenoble, June 6-9, 2017.

3. The Tianyuan Spring school, Beijing, March 13-18, 2017.

4. The workshop “Newton-Okounkov Bodies, Test Configurations, and Diophantine Geometry”, Banff, February 5-10, 2017.