- Algebra and Algebraic Geometry
- Analysis
- Applied Mathematics
- Combinatorics
- Computer Science
- Differential Equations
- Financial and Actuarial Mathematics
- Geometry & Topology
- Logic and Foundations
- Mathematical Biology
- Mathematical Physics
- Mathematics Education
- Number Theory
- Probability Theory
- Research Training Grant
- Named Postdoctoral Fellows

#### Annotated List of All RTG Graduate Student Fellows

This appendix contains a complete annotated list of every graduate student in our group who has received at least one semester of RTG support.

Over the tenure of our current RTG, we have supported 20 graduate student fellows. This works out to roughly 4-5 students each semester for nine semesters. The median number of semesters of RTG support has been two, though some students received up to five semesters of support. All RTG fellows have been US citizens or permanent residents, and eleven have been women or US minorities. Of the 20 RTG fellows, eleven have already completed the PhD.

We are especially proud of the quality of these graduates: in each of the four years since our RTG program was established, an RTG Graduate Fellow and member of our group has been awarded Michigan's Sumner Myers prize for the best thesis of the year. In fact, one won the highly competitive University-wide Distinguished Dissertation award. Of the eleven graduates, one was awarded a Clay Fellowship, and three were awarded NSF post-doctoral fellowships. Nine are employed in post-doctoral positions in strong academic departments, one will begin soon at NSA and one works for Google.

We now briefly describe each of our graduate student fellows, beginning with those who will have already completed the PhD:

- Sam Payne defended his thesis "Toric Vector Bundles" in 2006, under the direction of Bill Fulton. He was the 2006 Math Department Sumner Myers thesis prize recipient. Sam currently holds a prestigious 5 Year Clay Fellowship, based at Stanford University.
- Cornelia Yuen defended her 2006 thesis "Jet schemes of monomial and determinantal ideals", written under the direction of Karen Smith, and then accepted a post-doctoral position at the University of Kentucky. Since then she has landed a tenure track assistant professorship at SUNY, Potsdam.

- Bryden Cais's 2007 PhD thesis "Compatibilities, correspondences, and integral structures in p-adic cohomology" was our second RTG-supported Sumner-Myers prize-winning thesis. Currently a CRM-ISM Postdoctoral Fellow at McGill, Bryden is an example of one of our "boundary" students: though a number theorist who worked with Brian Conrad, Bryden was an active participant in many of our group's RTG-supported activities, and worked under the close mentorship of RTG PI Karen Smith.

- Janis Stipins ﬁnished a 2007 PhD "On Finite k-Nets in the Complex Projective Plane" under the direction of Igor Dolgachev and now works for Google.

- Susan Sierra's 2008 PhD thesis "The Geometry of Birationally Commutative Graded Domains" won not only our department's Sumner Myer's thesis prize, but also the university wide Distinguished Dissertation Award as well. Another "boundary member" of our group, Sue's advisor was Toby Staﬀord, though she was a very active participant who interacted widely with faculty and students in our group.

- Yogesh More wrote his 2008 PhD thesis "Arc valuations on smooth varieties," under the direction of Karen Smith, with heavy inﬂuence also from Mircea Mustat¸ˇa. He is currently a post-doc at the University of Missouri, working closely with Dan Edinin.
- Hanna Robbins worked est University. with Mel Hochster, ﬁnishing her thesis "Finiteness of Associated Primes of Local Cohomology Modules" in 2008. She is currently an assistant professor at Wake For
- Dave Anderson has just completed his thesis "Degeneracy Loci and G2 Flags" under the direction of Bill Fulton, and has accepted an NSF post-doctoral fellowship to work with Sara Billey at the University of Washington in Seattle starting in Fall 2009.
- Kyle Hofmann has just completed his thesis "Triangulation of Locally Semi-Algebraic Spaces" under the direction of Mircea Mustata, and will join the ranks of the National Security Agency summer 2009.
- Jonathan Bober will defend his thesis "Integer Ratios of Factorials, Hypergeometric Series, and Related Step Functions" this June, under the direction of JeJefrey Lagarias. In September, he will begin a post-doctoral position at the Institute for Advanced Study in Princeton.
- Paul Johnson
^{3 }defended his thesis "Equivariant Gromov-Witten Theory of One Dimensional Toric Stacks" last month, and will be awarded the department's Sumner Myer's prize for the best math PHD thesis of 2009. He worked with Yongbin Ruan, and has also been supported by the department's Geometry and Topology RTG. He has accepted an NSF post-doctoral fellowship to work with Rahul Pandharipande at Princeton University.

We are extremely proud of the talent and diversity of the current crop of RTG graduate fellows as well:

- Kevin Tucker, who is working with Karen Smith on multiplier ideals and will finish next year (2010), already has three papers accepted or submitted, including one coauthored with post-doc Karl Schwede. He is a leader among our students, frequently organizing the student seminar, speaking in the post-doc seminar, teaching younger students, and co-organizing one workshop.
- Kelli Talaska will complete her thesis with Sergey Fomin, "Total positivity and the Grassmannian" in 2010. Among her many publications are three preprints produced with RTG support. RTG support has allowed her to travel to several international conferences to present her work and to meet with collaborators.

- Beth Chen is working with Jeffrey Lagarias on Hilbert's 18-th problem. Her first paper "A dense packing of regular tetrahedra," has just appeared. She is ready to graduate later this year.

- Brian Jurgelwicz is working with Igor Dolgachev on the McKay correspondence and is on schedule to complete his PhD in 2010.

- Jose Gonzalez is working with Mircea Mustata on toric varieties and is expected to ﬁnish in 2010.

- Chelsea Walton works with Toby Staﬀord and Karen Smith. Her ﬁrst paper "Classiﬁcation of Degenerate Sklyanin Algebras" was recently accepted for publication in the Journal of Alegbra, and we expect her to ﬁnish in 2011. A natural leader, Chelsea is a very visible African-American student who has organized support networks for women .
- Daniel Hernandez is working with Karen Smith on computing F-thresholds, and is expected to ﬁnish in 2011. Daniel has been proactive in mentoring minority students at Michigan; among other activities, he has been an instructor for our M-STEM program for entering at-risk undergraduate students.

- Emily Witt is writing her thesis with Mel Hochster on local cohomology of determinantal ideals. She is expected to finish in 2011.
- Harlan Kadish is the newest addition to our RTG group. Recently promoted to candidacy, he will work with Harm Derksen, most likely on quiver representations.

Of course, our graduate student cohort includes a number of international and visiting students who enhance the diversity of our program. Experience shows that many of these eventually become permanent US residents and remain in the US in academics and industry. Currently, the international PhD students in the core algebraic geometry group include: Alan Stapledon (from Australia, 2009 Mustata) who has accepted a position at the University of British Columbia, Shin-Yao Jow (from China, 2009, Lazarsfeld) who has accepted a posts-doctoral position at UPenn, Marc Krawitz (South African, 2010 expected, Yongbin Ruan) Eugene Eisenstein (Canadian PhD expected 2011, Lazarsfeld), Victor Lozavanu (Moldovian PhD expected 2010, Lazarsfeld). Although none of these students have been directly funded by the RTG, all have benefitted by the numerous RTG activities, conferences and workshops, and the pool of collaborators the RTG provides. RTG funding has also increased the overall funding level for graduate student travel, freeing up other resources for funding all students' travel and support.