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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