- 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
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- Algebraic Geometry - Research Training Grant (RTG)
- Geometry, Topology and Dynamics - Research Training Grant (RTG)
Project Summary Training the Research Workforce in Geometry, Topology and Dynamics
This proposal calls for a research training program in geometry, topology and dynamics at the University of Michigan. Recent Ph.D.’s and advanced graduate students will be the main beneficiaries. We will deepen and broaden their training and give the trainees ample opportunities to excel in their research. Five senior faculty members (Mario Bonk, Richard Canary, John Erik Fornaess, Juha Heinonen and Ralf Spatzier) will lead this project in collaboration with eleven other senior faculty in these areas at Michigan.
Intellectual Merit: Topology, geometry and dynamical systems are core areas in mathematics. Especially in recent years, they have developed in mutually beneficial interaction. Many of the most exciting developments in these areas are truly interrelated, and benefit from each other either by idea, analogy or actual tool. At the same time, connections with other fields such as algebraic geometry and mathematical physics have strengthened dramatically. These developments have been amazing in their breadth and depth, and demonstrate the vitality of these areas. Completely new areas have arisen in the last two decades.
Broader Impact: The Mathematics Department at the University of Michigan has one of the largest and most vigorous post-doctoral and graduate programs in the country. It has an excellent record of producing high-quality researchers in geometry, topology and dynamics. This proposal calls to bolster the training of post-docs and graduate students in geometry, topology and dynamics by deepening and broadening it. In particular, we propose the following specific innovations in our training:
- Overhaul our seminars by introducing Intensive, Exploratory and Conjecture seminars.
- Introducing a new Explorations in Geometry, Topology and Dynamics Seminar.
- Hold workshops specifically geared at young researchers.
- Present numerous opportunities for advanced graduate students and post-docs to develop their lecturing skills.
- Provide for travel semesters to other prominent research places.
- Mentor graduate students and post-docs on their research, teaching and careers.
- Offer undergraduates intensive research experiences in the three areas.
RTG Graduate Students*
Emily Clader (ETH Zurich, Assist. Prof. San Francisco State Univ.)
David Constantine (Univ. Chicago, Assist. Prof. Wesleyan Univ.)
Dondi Ellis
William Gignac (Ecole Polytechnique, Georgia Tech.)
Jasun Gong (Univ. Pittsburgh, Assist. Prof. Fordham Univ.)
Chris Hammond (Texas A&M)
Becky Hoai (Federal Reserve Bank of St. Louis)
Paul Johnson (Imperial College, Sheffield)
Daniel Kneezel
Sara Lapan (Northwestern Univ., Assist. Prof. UC Riverside)
Robin Lassonde (software: East Agile, now Google)
Michelle Lee (Univ. Maryland, GEICO)
Aaron Magid (Univ. Maryland)
Johanna Mangahas (Brown Univ., Assist. Prof. Univ. Buffalo)
Jeffrey Meyer (Univ. Oklahoma, Assist. Prof. Cal. State San Bernadino)
Kyle Ormsby (MIT, Asst. Prof. Reed College)
Nathan Priddis (Leibniz Universität, Assist. Prof. Hannover, BYU)
Rohini Ramadas (Harvard, NSF postdoc)
Felipe Ramirez (Bristol, Assist. Prof. Wesleyan Univ.)
David Renardy (Invincea Labs)
Russell Ricks (SUNY Binghamton)
Geoffrey Scott (Univ. Toronto)
Brandon Seward (Hebrew Univ., NYU)
Mark Shoemaker (Univ. Utah, Assist. Prof. Colorado State University)
Robert Silversmith (Stony Brook-Simons Center)
Diane Vavrichek (CNA)
Nina White (SOE lecturer Univ. Michigan, Lecturer Univ. Michigan)
Kevin Wildrick (University of Jyvaskyla, Assist. Prof. Montana State University)
Marshall William (Univ. of Illinois at Chicago)
Crystal Zeager (McKinsey)
Andrew Zimmer (Univ. Chicago, NSF postdoc; Assist. Prof. William and Mary)
*The field in parentheses indicates the students's appointment following their time at Univ. Michigan.
RTG Postdoctoral Fellowships*
Patrick Boland (Lecturer Univ. Mich.)
Khalid Bou-Rabee (Assist. Prof. The City College of New York)
William Breslin (Assoc. Prof. Pacific University)
Harrison Bray (current)
Jeffrey Brown (IBS- Center for Geometry and Physics (Postech Campus))
Trevor Clark (Research Assoc. Imperial College London)
Matthew Durham (current)
Joel Fish (Standford, Assist. Pro.f U Mass Boston)
Dusty Grundmeier (Ball State University)
Mark Hagen (Postdoc. Cambridge Univ., Bristol University)
Jonathan Handy (unavail.)
Diana Hubbard (current)
Rohan Kadakia (current)
Michael Kelly (CCR)
Paul Kessenich (Lecturer Univ. Mich.)
Yvonne Lai (Assist. Prof. Univ. Nebraska)
Ben Linowitz (Assist. Prof. Oberlin College)
Lars Louder (Lecturer University College London)
Anton Lukyanenko (Assist. Prof. George Mason)
Christopher Mooney (Assist. Prof. Bradley Univ.)
Alexandra Pettet (Assoc. Prof. UBC)
Mark Radosevich (Lecturer Univ. Mich. Dearborn)
Paul Reschke (SBB Research Group)
Dustin Ross (Assist. Prof., SFSU)
Sonmez Sahutoglu (Assist. Prof. Univ. of Toledo)
Kevin Schreve (NSF postdoc, U Michigan)
Sohrab Shahshahani (Assist. Prof. Univ. Mass.)
David Sher (Assist. Prof. DePaul Univ.)
Matthew Stover (Assist. Prof. Temple Univ.)
Daniel Visscher (Lecturer U Mich. , Assist. Prof, Ithaca College)
Nicholas Vlamis (current)
*The field in parentheses indicates the fellow's appointment following their time at Univ. Michigan.
RTG Supported Theses
| Dondi Ellis | 2017 | Motivic Analogues of MO and MSO |
| Rohini Ramadas | 2017 | Dynamics on the Moduli Space of Pointed Rational Curves |
| Robert Silversmith | 2017 | A Mirror Theorem For Symmetric Products of Projective Space |
| David Renardy | 2016 | Bumping in the Deformation Spaces of Hyperbolic 3-Manifolds with Compressible Boundary |
| Brandon Seward | 2015 | Krieger’s Finite Generator Theorem For Ergodic Actions Of Countable Groups |
| Russell Ricks | 2015 | Flat Strips, Bowen-Margulis Measures, And Mixing Of The Geodesic Flow For Rank One Cat(0) Spaces |
| Nathan Priddis | 2014 | A Landau-Ginzburg/Calabi-Yau Correspondence For The Mirror Quintic |
| Becky Hoai | 2014 | On Symplectic Invariants Associated To Zoll Manifolds |
| Andrew Zimmer | 2014 | Rigidity Phenomena In Complex Projective Space |
| Emily Clader | 2014 | The Landau-Ginzburg/Calabi-Yau Correspondence For Certain Complete Intersections |
| Geoff Scott | 2014 | Torus Actions And Singularities In Symplectic Geometry |
| Mark Shoemaker | 2013 | A Mirror Theorem for the Mirror Quintic |
| William Gignac | 2013 | Equidistribution of Preimages in Nonarchimedean Dynamics |
| Jeffrey Meyer | 2013 | On the Totally Geodesic Commensurability Spectrum of an Arithmetic Locally Symmetric Spaces |
| Sara Lapan | 2013 | On the existence of attracting domains for maps tangent to the identity |
| Jordan Watkins | 2013 | The Higher Rank Rigidity Theorem for Manifolds with No Focal Points |
| Jordan Sahattchieve | 2012 | Solutions to Two Open Problems in Geometric Group Theory |
| Robin Lassonde | 2012 | Splittings of Non-Finitely Generated Groups |
| Michelle Lee | 2012 | Dynamics on the PSL(2, C)-character variety of certain hyperbolic 3-manifolds |
| Nina White | 2012 | Bounds on eigenvalues of the Laplacian for certain classes of closed hyperbolic 3-manifolds |
| Daniel Kneezel | 2011 | Verlinde K-theory |
| Kyle M. Ormsby | 2010 | Computations in stable motivic homotopy theory |
| Felipe Ramirez | 2010 | Smooth Cocycles over homogeneous dynamical systems |
| Marshall Williams | 2010 | Metric Currents and Differentiable Structures |
| Johanna Mangahas | 2010 | On Subgroups of Mapping Class Groups |
| Paul Johnson | 2009 | Equivariant Gromov-Witten Theory of One Dimensional Toric Stacks9 |
| Aaron Magid | 2009 | Deformation Spaces of Kleinian Surface Groups are not Locally Connected (pdf) |
| Christopher Hammond | 2009 | Invariants of Transformation Groups Acting on Real Hypersurfaces of Complex Spaces (doc) |
| David Constantine | 2009 | Hyperbolic rank-rigidity and frame flow (doc) |
| Jasun Gong | 2008 | Derivations on Metric Measure Spaces (doc) |
| Kevin Wildrick | 2008 | Quasisymmetric parameterizations of two-dimensional metric spaces |
| Diane Vavrichek | 2008 | Accessibility and JSJ decompositions of group (doc) |
RTG Workshops & Lecture Series
| May 29 - June 2, 2017 | Mirror Symmetry Conference for Young Researchers | |
| December 3-6, 2015 | Arithmetic Dynamics | |
| November 10-14, 2014 | A.Pixton - Tautological Relations on Moduli Spaces of Smooth Curves | |
| April 25-27, 2014 | Thin Groups Workshop Thin Groups Lectures | |
| March 10-13, 2014 | S. Dyatlov - Microlocal Analysis in Dynamics and Relativity | |
| March 3-7, 2014 | B-model aspects of Gromov-Witten Theory | |
| March 29-31, 2013 | Random Walks on Groups | |
| March 4-8, 2013 | Geometry and Physics of Gauged Linear Sigma Model | |
| December 7-9, 2012 | Complex and Non-Archimedean Dynamics | |
| May 4-6, 2012 | Recent Progress on Hyperbolic 3-manifolds | |
| February 18-19, 2012 | Mirror Symmetry | |
| February 16-24, 2012 | K. Hori - Mirror Symmetry from a Physical Perspective | |
| October 8-9, 2011 | Topics in Several Complex Variables and CR Geometry | |
| October 24-27, 2011 | A. Lubotzky - Expanders and Sieve Methods | |
| September 26-29, 2011 | K. Fukaya - Lagrangian Floer Homology and Mirror Symmetry | |
| April 15-17, 2011 | Higher Dimensional Teichmueller Theory | |
| April 1-3, 2011 | Some Topics in Geometric Function Theory of Several Complex Variables | |
| March 2011 | Heegaard Floer meets Seiberg--Witten | |
| April 2010 | Cobordism and Madsen-Weiss' Theorem | |
| April 2010 | Gromov-WittenTheory and Related Topics | |
| March 2010 | Holomorphic Maps and Iterations | |
| December 2009 | Complex Dynamics | |
| April 2009 | Geometric Group Theory | |
| April 2009 | Recent Developments in Oka Theory | |
| April 2008 | Dynamics of Teichmuller Theory | |
| December 2007 | CR Geometry | |
| April 2007 | Geometry of Teichmuller Theory |
RTG Supported Publications
All Years - RTG Bibliography (pdf)
2017 RTG Bibliography (pdf)
2016 RTG Bibliography (pdf)
2015 RTG Bibliography (pdf)
2014 RTG Bibliography (pdf)
2013 RTG Bibliography (pdf)
2012 RTG Bibliography (pdf)
2011 RTG Bibliography (pdf)
2010 RTG Bibliography (pdf)
2009 RTG Bibliography (pdf)
2008 RTG Bibliography (pdf)
