## J.L. Doob Postdoctoral Program

To apply for a postdoctoral position, please see our job listings.

This program, named in honor of mathematics Professor Emeritus Joseph L. Doob, began in Fall 1997 with two appointees. Appointees are named J. L. Doob Research Assistant Professors. Each appointment is for a three-year term and is non-renewable. By 1999, there were six permanent J.L. Doob postdoctoral appointees on campus. Every year, two or three new appointments can be made. The Mathematics faculty act as mentors and collaborators for the postdoctoral appointees.

#### 2016-2019 J. L. Doob Research Assistant Professors

**Emily Cliff** grew up in Edmonton, Canada, where she studied for her BA in linguistics and mathematics
at the University of Alberta. After deciding to focus on pure mathematics, she moved to the University
of Toronto to complete her MSc, and then to Oxford to work on her DPhil under the supervision of Kobi
Kremnizer, on chiral and factorization algebras and factorization spaces. She worked for a year in Oxford
as a junior research fellow in geometry and representation theory before coming to Illinois. When not
learning about math, Emily has been learning to play the cello (for the last year) and to do karate (for the
last twenty-one years). She also enjoys cooking and crafts such as knitting and quilting.

**Erik Walsberg** was raised in Pheonix, Arizona. He did his undergraduate degree in mathematics at Arizona
State University. He then moved to Los Angeles, where he completd his PhD in 2015 in the UCLA logic group under the supervision of Matthias Aschenbrenner. He then spent a year as a postdoc at the Hebrew University
of Jerusalem, although he was physically in Paris during that time. His research is in model theory, in
particular model theory over the real line. He has also dabbled a bit in metric geometry.

**Ying Wang** received her BS in pure and applied mathematics, a BA in economics, and an MS in probability
and statistics in China before she began her PhD in actuarial science at the University of Waterloo in 2016. She did research on the pricing and hedging for the variable annuities for her master’s degree, and then worked on the risk measures and capital allocation principles for risk management as a research assistant in Waterloo during which time she also obtained the designation of Associate of the Society of Actuaries (ASA) there. The research topics that she is focusing on now are new risk measures, capital allocation principles and
related applications. Besides her actuarial research interests, Wang likes painting, baking and traveling.

#### 2015-2018 J. L. Doob Research Assistant Professors

**Mark Bell** completed his PhD in 2015 at the University of Warwick under the supervision of Saul Schleimer. His research interests are in computational topology and geometric group theory. Specifically, he is interested in decision problems in low dimensional topology involving knots, surfaces and 3-manifolds. In his free time, Mark enjoys rock climbing and swimming.

**Daniel Berwick-Evans** received his PhD in 2013 from the University of California Berkeley under the supervision of Peter Teichner, and then spent two years at Stanford University as a Szego Assistant Professor. His research uses methods from quantum field theory to construct invariants of manifolds. An ideal vacation for him involves rock climbing and/or kayaking.

**Ivan Contreras** grew up in Bogota, Colombia. He obtained his undergraduate degree in mathematics in 2008 at Los Andes University, Colombia. In 2008 he moved to Utrecht, The Netherlands, to join the master class program “Aspects of Calabi-Yau geometries”. In 2009 he moved to Switzerland and in 2013 he completed his PhD under the guidance of Alberto Cattaneo in the University of Zürich. Before moving to our department, Ivan was appointed as a postdoctoral fellow at University of California, Berkeley for two years. His research interest is mathematical physics and differential geometry. In particular, he studies the interplay between symplectic, Poisson geometry, and classical, quantum field theories.

**Sergey Dyachenko** completed his undergraduate degree in PhysTech (MIPT) in Dolgoprudny, Moscow and received his PhD in 2014 in applied
mathematics from the University of New Mexico under the guidance of Pavel Lushnikov and Alexander Korokevich. Before
coming to Illinois he was a Visiting Assistant Professor at the University of Arizona where he
worked with Vladimir Zakharov and Alan Newell. His research is concentrated on numerical simulations of systems that admit
singular solutions, in particular evolution of water waves that lead to overturning, and simulations of blowing up solutions
in nonlinear optical media.

**Laura Escobar** grew up in Colombia, where she did her undergraduate degree in mathematics. She completed her PhD in 2015 at Cornell University under the supervision of Allen Knutson. Her research interests are combinatorics, algebraic geometry and the interactions between these areas. In particular she studies Schubert varieties. In her spare time she enjoys reading, hiking and traveling.

**Nicolas M. Robles** (PhD 2015, Universität Zürich) studied mathematics and physics at Imperial College and Cambridge. He also worked in investment banking in London and Zurich (JPMorgan, Nomura and UBS), before deciding to go back to graduate school for a doctorate in analytic number theory under the joint supervision of Alberto Cattaneo and Ashkan Nikeghbali. Away from work, he likes golf, skiing, soccer, history, board games and movies.

**Rebecca Tramel** grew up in Massachusetts, and did her undergraduate degree at Smith College as a double major in Mathematics and French language. She then completed her masters at the University of Connecticut, and received PhD in 2015 from the University of Edinburgh, where she studied under Arend Bayer. Her research interests are algebraic geometry and derived categories. In particular, she is interested in connections between algebraic geometry and Bridgeland stability conditions. Her hobbies include cooking, running, and exploring the Urbana-Champaign area with her husband and their Australian shepherd, Sabrina.

**Jing Wang** completed her PhD in 2014 from Purdue University under the supervision of Fabrice Baudoin. Before coming to Illinois, she spent one year as a postdoc fellow at IMA, University of Minnesota. Her research interest lies in the intersection of probability and sub-Riemannian geometry. In particular she works on diffusions on sub-Riemann manifolds; and heat kernel estimates of degenerate hypoelliptic diffusions. During her spare time, she enjoys dancing and teaching Salsa (a latin social dance) and Argentina tango.

**Ming Xiao** Before coming to U.S, Ming Xiao did his undergraduate degree in Mathematics from University of Science and Technology of China. He completed his PhD at Rutgers University in May 2015. He works in the fields of several complex variables, Cauchy Riemann geometry, complex geometry. His current research includes mapping problems in CR geometry and several complex variables, complex geometry of bounded domains in complex Euclidean spaces, applications of PDEs to complex analysis. Outside of Mathematics, he is a fan of soccer and likes watching soccer matches.

**Xin Zhang** obtained his PhD from Stony Brook in 2014, under the guidance of Prof. Alex Kontorovich. He spent one year at Tel Aviv University before coming to Illinois. His current research lies in analytic number theory, spectral theory, homogeneous dynamics and the interplay between them. In his spare time, he likes to play tennis, badminton and ping pong.

#### 2014-2017 J. L. Doob Research Assistant Professors

**Cary Malkiewich** (PhD 2014, Stanford University) hails from Worcester, Massachusetts, and got his bachelors degree from Princeton University. He completed
his PhD at Stanford University under the direction of Ralph Cohen. Cary’s research interests lie broadly in algebraic topology
and smooth manifolds. He has recently studied applications of calculus of functors to string topology, and how both algebraic
K-theory of spaces and topological Hochschild homology interact with Koszul duality. In his free time Cary enjoys running,
cooking, retro gaming, and spending time with his wife.

**Alexander Miller** grew up in Minnesota and got his PhD in 2013 from the University of Minnesota. He is interested in combinatorics
and reflection groups.

Hailing from Thailand, **Detchat Samart** (PhD 2014 Texas A & M University) attended Texas A&M University in 2009 as a doctoral student. Before that he received his
bachelor’s degree in mathematics from Chulalongkorn University in Bangkok. He completed his PhD in 2014 under the
supervision of Matthew Papanikolas. His research focuses on Mahler measures and its connection with values of L-functions
and other special functions. He is also interested in modular forms and arithmetic of algebraic varieties. During the Spring 2015
semester, he will visit the Centre de Recherches Mathématiques in Montreal and return to Illinois for the Fall 2015 semester.
Besides doing math, he also enjoys music-related activities, travelling, and playing ping pong.

**Jenya Sapir** completed her PhD in 2014 from Stanford University under the supervision of Maryam Mirzakhani. Her research interests are
in low dimensional topology and geometric group theory. Specifically, she is interested in the various ways to study curves on
surfaces. In her free time, Jenya enjoys backpacking and ceramics.

#### 2013-2016 J. L. Doob Research Assistant Professors

Ikemefuna Agbanusi obtained his PhD in 2013 at Boston University. His research interest is in partial differential equations and most especially in boundary value problems, Schrödinger operators and geometric applications. When he is not doing mathematics, Ike likes to spend time cooking, hiking and running.

Ioan Marcut grew up in the town of Sibiu in Romania. He obtained his undergraduate degree in mathematics in 2007 at Babes-Bolyai University, Cluj, Romania. In 2007 Ioan moved to Utrecht, The Netherlands, where he joined the master class program “Quantum Groups, Affine Lie Algebras and their Application.” During 2008–2012 he was a PhD student under the guidance of Marius Crainic in Utrecht, where he continued his research as a postdoctoral fellow, before joining our department in August 2013. Ioan’s research is in the field of differential geometry, more specifically, he studies Poisson manifolds. Poisson geometry lies at the intersection of three very active areas of mathematics, namely Symplectic Geometry, Foliations and Lie Theory.

Theodore Molla completed his PhD under the supervision of Henry Kierstead and Andrzej Czygrinow at Arizona State University in 2013. Prior to his PhD he worked as a computer programmer in the greater Phoenix Area. His research is in graph theory with an emphasis on directed graphs and extremal problems.

Laura Schaposnik grew up in La Plata, Argentina, where she did her undergraduate degree in Mathematics. She moved to England in 2008 and completed her PhD in 2013 from the University of Oxford under the supervision of Nigel Hitchin. Before coming to Illinois, she spent a year as a Wissenschaftlicher Assistent at Universität Heidelberg, Germany. Her research interest is on the moduli space of Higgs bundles and its relation to representation theory, algebraic geometry and mathematical physics. During her spare time, she enjoys teaching math in schools, cooking, taking photos for her Project 365 and exploring new cities.

Anush Tserunyan grew up in Yerevan, Armenia, where she received her undergraduate and Master’s degrees in computer science from Yerevan State University. She completed her PhD in mathematics at UCLA under the supervision of Alexander Kechris (Caltech) in 2013. Her research lies in descriptive set theory, and focuses on the theory of definable equivalence relations and its applications in ergodic theory and topological dynamics. In her free time, she either plays piano and tries to compose. If she is forced to exercise, she does fencing.

#### 2012-2015 J. L. Doob Research Assistant Professors

Michael Brannan grew up in the town of Saint Catharines, Ontario, Canada, and completed his Ph.D. in 2012 at Queen's University, Kingston under the supervision of James Mingo and Roland Speicher. His research interests include operator algebras, quantum groups, non-commutative harmonic analysis, and free probability.

Francesco Cellarosi grew up in Italy, and obtained his undergraduate degree in mathematics in 2006 from the Universita' di Bologna. He then moved to the United States, where he received his Ph.D. from Princeton University in 2011 under the supervision of Yakov G Sinai. Recently, he spent one year between the Institute for Advanced Study in Princeton NJ and at the Mathematical Sciences Research Institute in Berkeley CA. His research focuses on the interplay between dynamical systems, number theory, and probability theory.

Ali Kavruk completed his Ph.D. at the University of Houston in 2010 and continued his research as a Post-Doctoral fellow for a year before joining our department. His doctoral dissertation focuses on tensor products on the algebra of operators with various applications in functional analysis as well as mathematical physics. He has conducted several research projects with mathematicians from United States, Canada and Europe. His current research interests mainly focus on Quantum Information Theory on both the theoretical and experimental level.

Derrick Stolee received his Ph.D. in Mathematics and Computer Science from the University of Nebraska–Lincoln under the supervision of Stephen G. Hartke and Vinod Variyam in 2012. He works in graph theory and combinatorics and specializes in computational methods.

Armin Straub is originally from Heusenstamm, Germany, but has spent five years in New Orleans at Tulane University, completing his Ph.D. in 2012 under the direction of Victor Moll. A semester and two summers of that time he spent at Newcastle University working with Jonathan Borwein. Armin's research has a focus on the many aspects of special functions, especially hypergeometric and modular ones, and he enjoys working on problems highlighting their connections to number theory, combinatorics and computer algebra. During the year of 2013 he will visit the Max Planck Institute for Mathematics in Bonn before returning to Illinois for the Spring 2014 semester.

Bogdan Udrea received his Ph.D. in 2012 from the University of Iowa, under the joint supervision of Paul Muhly and Ionut Chifan. His thesis contains some results about structural properties of type II1 factors coming from actions of direct products of hyperbolic groups. His research interests include classification and structural theory of von Neumann algebras, particularly those coming from group actions on measure spaces, C*-algebras theory and ergodic theory.

Ben Wyser received his Ph.D. in mathematics from the University of Georgia in 2012 under the advisement of William Graham. His research interests are primarily in algebraic groups and the geometry and combinatorics of homogeneous spaces, flag varieties and symmetric spaces in particular. Originally from Mississippi, Wyser spent three years as a computer programmer in Arkansas before moving to Georgia for graduate school.

#### 2011-2014 J. L. Doob Research Assistant Professors

Spencer Dowdall received his Ph.D. in 2011 from the University of Chicago under the direction of Benson Farb. Dowdall's research interests are in geometric topology, mapping class groups, Teichmüller theory, and geometric group theory.

Jingwei Guo received his Ph.D. in 2011 from the University of Wisconsin at Madison under the direction of Andreas Seeger. His research interest is in harmonic analysis. In particular he is interested in its applications to the lattice point problem and other problems in analytic number theory.

Xiannan Li received his Ph.D. from Stanford in 2011. His advisor was Kannan Soundararajan. Li's broad area of interest is analytic number theory and his recent research has involved L-functions.

Bernard Lidicky received his Ph.D. in 2011 from Charles University, Prague, under the direction of Jiri Fiala. His research interests are in graph theory and discrete algorithms.

#### 2010-2013 J. L. Doob Research Assistant Professors

Philipp Hieronymi received his DPhil from the University of Oxford in 2008 under the supervision of Alex Wilkie. Before coming to Illinois, he spent a year as a DAAD fellow at the Fields Institute and McMaster University. His research in logic focuses on ordered structures and their potential applications in analysis and geometry.

Youness Lamzouri received his Ph.D. from the University of Montreal in 2009 under the supervision of Andrew Granville. Before coming to Illinois, he held a postdoctoral appointment at the Institute for Advanced Study at Princeton. His research interests are in analytic, combinatorial and probabilistic number theory. He recently studied the distribution of extreme values of the Riemann zeta function and L-functions in the critical strip.

#### 2009-2012 J. L. Doob Research Assistant Professors

Dr. Isidora Milin completed her Ph.D. in 2008 at Stanford University, under the supervision of Yasha Eliashberg. Her thesis dealt with contact dynamics and groups of contactomorphisms. During the 2008-09 school year, she was a postdoctoral fellow at The School of Mathematical Sciences at Tel Aviv University in Israel. Her research interests lie in symplectic and contact geometry and Hamiltonian dynamics.

#### 2008-2011 J. L. Doob Research Assistant Professors

Dr. N. Elizabeth Csima received her Ph.D. in 2008 from the University of Chicago. Her dissertation was completed last June under the supervision of Robert Kottwitz. It dealt with the study of F-crystals. Her research interests lie in algebraic geometry and number theory, particularly questions which arise from the study of Shimura varieties.

Dr. Pierre Fima received his Ph.D. in 2007 from the University of Caen, France, under the direction of Professor Leonid Vainerman. He did his graduate studies in Ecole Normale Superieure and in Denis Diderot University in Paris. He worked for one year in the University of Besancon as a post doctoral researcher before coming to Illinois. His research interest lies at the intersection of operator algebras and quantum groups theory.

Dr. Bertrand Guillou received his Ph.D. from the University of Chicago in 2008 under the supervision of J. Peter May. His research interests are in homotopy theory, especially motivic and equivariant homotopy theory.

Dr. John Mackay received his doctorate from the University of Michigan in 2008, under the supervision of Professor Bruce Kleiner. He also spent most of the last two years visiting his advisor at Yale. His research interests include geometric group theory, analysis on metric spaces and topics involving the word "Gromov."

Dr. Bartlomiej Siudeja received his Ph.D. in 2008 at Purdue University under supervision of Professor Rodrigo Bañuelos. He received his MS degree at Wroclaw University of Technology. His dissertation was a mixture of stochastic processes and planar eigenvalue problems. He is actively pursuing both of those topics at Illinois.

#### 2007-2010 J. L. Doob Research Assistant Professors

Dr. Jiri Lebl received his Ph.D. in 2007 from the University of California at San Diego under the supervision of Peter Ebenfelt. Lebl is currently interested in CR geometry (several complex variables) and most things related. Lebl was born in Prague when it was still Czechoslovakia but has lived in the U.S. since 1991.

Jeremy Rouse , a native of California, received his Ph.D. at the University of Wisconsin-Madison in 2007 under the direction of Ken Ono. Rouse's research interests involve elliptic curves, modular forms, analytic number theory, and the relationships between them.

Andrew Schultz received his Ph.D. in 2007 from Stanford University. As an undergraduate, Schultz worked with John Swallow at Davidson College, studying the Galois module structure of certain invariants of fields. He continued this work in his Ph.D. dissertation under the direction of Ravi Vakil at Stanford University, where he was also interested in exploring further connections to algebraic geometry and algebraic K-theory.

Sujith Vijay received his doctorate in 2007 from Rutgers University under the supervision of Professor Jozsef Beck. His dissertation dealt with arithmetic progressions, and his research interests lie at the intersection of combinatorics and number theory.

#### 2006-2009 J. L. Doob Research Assistant Professors

Dr. Tao Mei, a native of China, received his Ph.D. from Texas A&M under the supervision of Dr. Gilles Pisier in 2006. Before he came to the U.S. in 2003, he spent one year in Besancon, France as a visiting scholar. His current research area concerns both functional analysis and harmonic analysis, especially in generalizations of classical results from harmonic analysis to operator valued (matrix valued) functions and related subjects, such as noncommutative martingales.

Dr. Julien Melleray received his Ph.D. in 2005 from Universite Paris 6 under the direction of advisor Jean Saint Raymond. His current research interests are linked with the study of Urysohn's universal Polish metric space and its applications to descriptive set theory and functional analysis. He is especially interested by the study of the isometry group of this space, and by the study of the geometry of its (uniquely determined) closed linear span.

#### 2005-2008 J. L. Doob Research Assistant Professors

Dr. Zoi Rapti studied in Athens, Greece where she received a B.S. in Mechanical Engineering. She then attended the University of Massachusetts at Amherst where she received her Ph.D. in Mathematics in 2004. After that she spent one year in Princeton, NJ at the Institute for Advanced Study. Her research interests are in applied mathematics. She has been studying the thermodynamics of nonlinear models for DNA denaturation using a transfer operator approach, and instabilities of the Nonliner Schrodinger Equation using dynamical systems methods.

#### 2004-2007 J. L. Doob Research Assistant Professors

Dr. Nora Ganter received her Ph.D. in 2004 from MIT. Ganter's research interests are in interactions of elliptic cohomology with other areas of mathematics. She has been working at a homotopy theoretic interpretation of the theory of orbifold elliptic genera and product formulas.

Dr. Mingchu Gao received his Ph.D. in 2004 from the University of New Hampshire. His research interests are in several areas of functional analysis: operator algebras, operator spaces and free probability.

Dr. Nicolas Guay received his Ph.D. in 2004 from the University of Chicago in the area of representation theory.

Dr. Panki Kim received his Ph.D. in 2004 from the University of Washington. His research interests are stochastic process, probabilistic potential theory and PDEs.

Dr. Arnd Lauber received his Ph.D. in 2004 from the University of Goettingen, Germany. His Ph.D. thesis was on the stability of Julia sets of transcendental function, which involves questions corresponding to the study of the Mandelbrot set for polynomials.

Dr. Young-Ran Lee received her Ph.D. in 2004 from the University of Alabama at Birmingham under the direction of Yulia Karpeshina. Her thesis title was "Spectral properties of a polyharmonic operator with limit-periodic potential in dimension two."

#### 2003-2006 J. L. Doob Research Assistant Professors

Dr. Emre Alkan received his Ph.D. in 2003 from the University of Wisconsin at Madison under the direction of Ken Ono. His research interests are automorphic and modular forms, and analytic number theory.

Dr. Christian Haesemeyer received his Ph.D. from Northwestern University in 2003 under the direction of Eric M. Friedlander. His research interests are algebraic K-theory, topology and geometry.

#### 2002-2005 J. L. Doob Research Assistant Professors

Dr. Alexander Berenstein received his Ph.D. from the University of Notre Dame. His field of research is model theory. Most of his thesis work was centered around defining a notion of independence inside structures related to Hilbert spaces.

Dr. Janne Heittokangas received his Ph.D. in 2000 from the University of Joensuu, Finland. He is interested in complex differential and functional equations, as well as all the other theories related to them.

#### 2001-2004 J. L. Doob Research Assistant Professors

Dr. Bernhard Lamel received his Ph.D. in 2000 from the University of California at San Diego. His research is in the area of geometry and several complex variables, with his primary interest in properties of mappings of real submanifolds in complex spaces of different dimensions. In 2001, he held a European Union Research Fellowship in Stockholm.

Dr. Jorge Rivera-Noriega received his Ph.D. from the University of Missouri at Columbia under the supervision of Dr. Steven Hofmann. His research interests are related to harmonic analysis and partial differential equations.

Dr. Evgueni Vassiliev received his Ph.D. from the University of Notre Dame under the direction of Professor Steven Buechler. His research field is mathematical logic, specifically model theory.

#### 2000-2003 J. L. Doob Research Assistant Professors

Dr. Luis Alvarez-Consul received his Ph.D. degree in 2000 from the University Autonoma of Madrid. His thesis title was "The Geometry of Dimensional Reductions in Gauge Theory." His research interests are in gauge theory and algebraic geometry.

Dr. Peter Brinkmann received his Dipl.-Math in 1997 from the University of Bonn. He has been a teaching fellow at the University of Utah, and has been a visitor at Henri Poincare Institute in Paris. His thesis title was "Mapping Tori o f Automorphisms of Hyperbolic Groups."

Dr. Marco Schlichting received his Ph.D. degree in 2000 from the University of Paris 7. His thesis title was "Delooping the K-Theory of Exact Categories and Negative K-Groups."

#### 1999-2002 J. L. Doob Research Assistant Professors

Dr. Wai Yan Pong has a 1999 Ph.D. degree from the University of Illinois at Chicago. His research advisor is David E. Marker . His thesis is concerned with applications of model theory to differential algebra and algebraic geometry.

Dr. Marcin Mazur has a 1999 Ph.D. degree from the University of Chicago. His research advisor was Spencer Bloch . His research interests are in number theory and group theory.

#### 1998-2001 The J. L. Doob Research Assistant Professors

Dr. Maria Basterra has a 1998 Ph.D. degree from the University of Chicago. Her thesis advisor was Peter May . Her main research interest is Algebraic Topology with Homological Algebra as a secondary interest. She received her undergraduate degree at the University of Texas at Austin in 1992.

Dr. Nadya Shirokova has a 1998 Ph.D. degree from the University of Chicago. Her thesis advisor was Shmuel Weinberger . Her major research interests are low-dimensional topology, singularity theory, and group actions on manifolds. She received her undergraduate education at Moscow University in Mathematics.

#### 1997-2000 J. L. Doob Research Assistant Professors

Dr. Tibor Szabó has a 1996 Ph.D. degree from The Ohio State University, earned under the supervision of Professor Ákos Seress . During 1996-97, he was a member of the Institute for Advanced Study in Princeton. His area of interest is extremal combinatorics. He received his undergraduate diploma with distinction from the Eötvös Loránd University of Sciences in 1990. In 1995 he was awarded the Presidential Fellowship of The Ohio State University.

Dr. Tadashi Tokieda has a 1996 Ph.D. degree from Princeton University. His advisor was William Browder . During 1996-97, he was a Postdoctoral Fellow and Lecturer at McGill University in Montreal. His interest is in symplectic topology and Hamiltonian dynamics. He is a 1989 classics graduate from Jochi University in Tokyo and has a 1991 bachelor degree from Oxford University in Mathematics.