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Florian EiseleView profile

Lecturer

• Modular Representation Theory
• Finite Group Algebras
• Algebra
• +3 more

Dr. Florian Eisele is a Lecturer in Pure Mathematics at the Department of Pure Mathematics, The University of Manchester. His research focuses on modular representation theory of finite groups and representation theory of finite-dimensional algebras. He holds a Doctor rerum naturalium (PhD) in Group Rings over the p-adic Integers from RWTH Aachen University, awarded in 2012. His research interests include finite group algebras, Picard groups, defect groups, and Zassenhaus conjectures. Notably, he has contributed to counterexamples in algebraic structures and explored topics like Morita Frobenius numbers and derived Picard groups. Eisele has published extensively on algebraic theories, including works on lattices, Hochschild cohomology, and Donovan’s conjecture. His 2021 Reinhold Baer Prize recognizes his impactful contributions. His articles frequently address advanced topics such as silting complexes, Tate duality, and block theory in modular representation contexts. He has investigated structures like generalized quaternion defect groups and 2-adic rings, contributing to the understanding of algebraic invariants and module theory. His work bridges abstract algebra with concrete examples, advancing both theoretical frameworks and specific problem solutions in representation theory.

Alan ReidView profile

Professor

• Hyperbolic Manifolds
• Low-Dimensional Topology
• Geometric Group Theory
• +2 more

Alan Reid is a Professor and Department Chair in Mathematics at Rice University . Previously, he served as the Pennzoil Company Regents Professor and Chairman at the University of Texas at Austin. His research focuses on hyperbolic manifolds , low-dimensional topology , and geometric group theory , with significant contributions to the arithmetic structure of Kleinian groups and profinite rigidity. Education: Ph.D. in Arithmetic Kleinian Groups, University of Aberdeen (1988) M.Sc. in Arithmetic Fuchsian Groups, University of Aberdeen (1985) B.Sc. (First Class Honours), University of Aberdeen (1984) Research Trends: Alan's work spans hyperbolic geometry , 3-manifold topology , and arithmetic hyperbolic manifolds . Recent publications examine profinite rigidity , surface subgroups , and geometric embeddings in higher dimensions. He has co-authored studies on thin subgroups , spin structures , and non-compact orbifolds . Scientific Awards: Alfred P. Sloan Research Fellowship (1997–2001) Fellow of the American Mathematical Society (2012) Corresponding Fellow of the Royal Society of Edinburgh (2024) Honorary Professor at IIT Guwahati (2024–2026) Advising and Grants: He has supervised over 20 graduate students, including prominent researchers now at institutions like Yale, Temple University, and the University of Minnesota. His work has been supported by grants from the National Science Foundation and collaborations with institutes such as MSRI, IAS, and MPIM Bonn.

• Discrete Subgroups of Lie Groups
• Algebraic Geometry
• Low-Dimensional Topology
• +5 more

Matthew Stover is a Professor in the Department of Mathematics at Temple University. His research spans discrete subgroups of Lie groups, algebraic geometry, low-dimensional topology, hyperbolic geometry, dynamics, and number theory, building on foundational work by Klein, Picard, and Poincaré through modern Gromov-Thurston and Margulis perspectives. Education: BA in Mathematics (University of Chicago, 2003); PhD in Mathematics (University of Texas at Austin, 2010). His work explores intersections of algebraic geometry with hyperbolic manifolds, focusing on congruence subgroups, superrigidity, and geometric group theory. Recent projects include cohomological nonvanishing for ball quotients and arithmeticity of complex hyperbolic manifolds. Recent publications (2021-2025) address topics such as totally geodesic submanifolds, residual finiteness, and Kähler groups. Keywords include hyperbolic geometry, algebraic fundamental groups, and geometric rigidity. Scientific Awards: 2023 Dean’s Distinguished Excellence in Research Award Grants include NSF DMS-2203555/2506896 and Simons Foundation SFI-MPS-TSM-00014184. He advises PhD students at Temple and collaborates on projects involving modular surfaces, Coxeter groups, and Shimura varieties.

Lvzhou ChenView profile

Assistant Professor

• Geometric Topology
• Geometric Group Theory
• Dynamics
• +3 more

Lvzhou Chen is an Assistant Professor of Mathematics at Purdue University's Department of Mathematics, part of the College of Science. His research focuses on geometric topology, geometric group theory, and dynamics, with specific interests in stable commutator length, mapping class groups of infinite-type surfaces, and their interplay with dynamical systems. He earned his Ph.D. in Mathematics from the University of Chicago (2020), advised by Danny Calegari, following an M.S. (2015) and B.S. (2014) from Fudan University and the University of Chicago. Prior to Purdue, he was a R. H. Bing Instructor (postdoc) at the University of Texas at Austin (2020–2022). Chen's research explores topics such as the geometry of infinite-type surfaces, quasimorphisms, and applications of stable commutator length to surface subgroups. His work bridges geometric group theory with low-dimensional topology and dynamical systems. He has contributed to prominent journals like *Invent. Math.*, *Trans. Amer. Math. Soc.*, and *Ergodic Theory and Dynamical Systems*. Key recent work includes studies on irrational rotations, Kervaire conjectures, and spectral gaps in groups. Chen advises graduate students, emphasizing rigorous weekly meetings and independent research training. He teaches advanced courses in linear algebra and topology, and actively participates in seminars such as the Geometry and Geometric Analysis Seminar and Topology Seminar at Purdue.

Miklós AbértView profile

Professor

• Measured group theory
• Asymptotic group theory
• Spectral theory of graphs and groups
• +7 more

Miklós Abért is a Professor at the MTA Alfréd Rényi Institute of Mathematics. His research focuses on measured and asymptotic group theory, with specific interests in spectral theory of graphs and groups, Benjamini-Schramm convergence, invariant random subgroups, homology growth, sofic entropy, and cellular automata. He leads the ERC Consolidator Grant research group "Asymptotic invariants of discrete groups, sparse graphs and locally symmetric spaces" (2015–present). Award of the Academy (2023) Rényi Prize (2017) János Bolyai Research Fellowship (2011) Erdős Pál Prize (2010) Grünwald Géza Memorial Medal (2003) His recent work explores the interplay between physical network structures, stochastic processes, and group-theoretic invariants, with applications to spectral radius analysis, torsion growth, and unimodular random trees. He has organized major conferences on measured group theory and collaborated extensively with leading mathematicians.

• Geometric Group Theory
• Algebra
• Topology
• +5 more

Dr. Olga Varghese is a Lecturer and Academic Advisor in the Department of Mathematics and Computer Science at the University of Münster since 2025. Her primary research focuses on geometric group theory, algebra, and topology, with a strong emphasis on Coxeter groups, automorphism groups, and CAT(0) spaces. She has held postdoctoral positions at the University of Münster (2015–2020) and DFG-funded roles at Heinrich Heine University Düsseldorf (2023–2025) and OvGU Magdeburg (2021–2023). She also served as a visiting scholar at the University of Chicago (2012–2013). PhD in Mathematics (2010–2015) and earlier studies (2005–2010) at the University of Münster Her research explores profinite properties, parabolic subgroups, graph products, and fixed point theorems in CAT(0) spaces. She has taught courses in topology, algebra, and geometry, including lectures on foundational and advanced topics. Her academic advisory service guides MSc Mathematics students in course selection and degree structure. She has presented at conferences in Münster, Cambridge, Cáceres, and Bielefeld, focusing on profinite rigidity and subgroup classification. Her publications span journals like Algebraic and Geometric Topology , Journal of Group Theory , and Communications in Algebra , addressing coherence, hyperbolicity, and automorphism group properties.

• Geometric Group Theory
• Algebra
• Topology
• +7 more

Dawid Kielak is a Professor of Pure Mathematics at the University of Oxford's Mathematical Institute and a Tutorial Fellow in Pure Mathematics at Hertford College, Oxford. His research bridges Geometric Group Theory and Algebra, with a focus on group rings, cohomology, and ℓ²-invariants. He is a member of the Algebra and Topology research groups and holds an ERC Starting Grant 'Fibring' (2019). His work explores properties like Kazhdan's T, BNSR invariants, and fibring in groups. Education: PhD in Mathematics from the University of Oxford (supervised by Martin Bridson), Habilitation thesis at Bielefeld University on 'Free groups, RAAGs, and their automorphisms'. Research interests include geometric and algebraic aspects of groups, with applications to 3-manifolds, hyperbolic geometry, and representation theory. His recent work addresses conjectures in group theory (e.g., Surface Group Conjectures), expands on ℓ²-Betti numbers, and investigates profinite rigidity. Publications span topics like coboundary expanders, quasi-BNS invariants, and algebraically hyperbolic groups, reflecting a focus on geometric and algebraic interplay. His articles often connect abstract group theory to topological and homological methods. Awards: Whitehead Prize (2022), ERC Consolidator Grant (2024), and multiple DFG/ERC grants. Advising: Supervises DPhil students in geometric group theory and algebra, including Gargi Biswas and Will Thomas. Labs/Teams: Coordinates a research group focusing on group theory and topology, with collaborations on projects involving random groups, RAAGs, and automorphisms.

Gareth WilkesView profile

Assistant Professor

• Profinite Groups
• Geometric Group Theory
• Geometric Topology
• +3 more

Dr. Gareth Wilkes is an Assistant Professor at the University of Cambridge, affiliated with Jesus College and Selwyn College. He holds positions as a Fellow at Jesus College and a Bye-Fellow at Selwyn College. His research focuses on the intersection of geometric group theory, geometric topology, and profinite groups, particularly exploring residual properties, profinite completions, and cohomological methods in these structures. Wilkes completed his doctoral studies at the University of Oxford in 2018 with a thesis titled Profinite Properties of 3-Manifold Groups . He is preparing a textbook Profinite Groups and Residual Finiteness (EMS, 2024), which provides a foundational treatment of profinite groups and their applications in residual finiteness studies. His work bridges algebraic and geometric perspectives, emphasizing group cohomology and profinite rigidity. His publications span topics such as profinite rigidity of 3-manifolds, cohomology theories for profinite groups, and the interplay between random groups and topological invariants like ℓ²-Betti numbers. Teaching materials, including lecture notes and exercises on profinite groups, are available for academic reference. Wilkes’ research also addresses accessibility of pro-p groups, profinite completions of geometric structures, and applications of finite quotients in distinguishing crystallographic groups.

Matthew JosephView profile

Lecturer

• Topological Dynamics
• Measurable Dynamics
• Ergodic Theory
• +5 more

Matthew Joseph is a mathematician specializing in topological dynamics, measurable dynamics, and ergodic theory. Starting September 1, 2025, he will serve as a Lecturer at IMJ-PRG (Institut de Mathématiques de Jussieu - Paris Rive Gauche), Paris-Cité University, where he maintains his office in room 709 of the Sophie Germain Building. His educational background includes doctoral studies at UMPA (Unité de Mathématiques Pures et Appliquées) from 2019-2022, where he completed his PhD under the supervision of Damien Gaboriau with a thesis titled "Topological and measurable dynamics: allostery, quantitative orbit equivalence." Prior to his doctorate, he attended École Normale Supérieure de Lyon from 2015-2019. Between 2022-2024, he held a postdoctoral position at Laboratoire Mathématique d'Orsay supported by FMJH (Fondation Mathématique Jacques Hadamard). Joseph's research focuses on the intersection of topological and measurable dynamics, with particular emphasis on allostery (actions that are topologically free but not essentially free), quantitative orbit equivalence, and the study of isometry groups of Urysohn spaces. His work explores the relationships between invariant random subgroups and uniformly recurrent subgroups, as well as the ergodic and analytic properties of permutation groups. He has made significant contributions to understanding dissociated permutation groups, stabilizer rigidity for ergodic actions, and the classification of unitary representations for isometry groups of rational Urysohn spaces. His publications span prestigious journals including Transactions of the American Mathematical Society, Fundamenta Mathematicae, and Ergodic Theory and Dynamical Systems. His recent work demonstrates a consistent focus on the connections between group-theoretic properties and dynamical behavior, with particular attention to how metric structures on orbits can be distorted while preserving essential dynamical features. Joseph actively contributes to the mathematical community through seminar organization, having co-organized the Groups and Actions Seminar (2023-2024, 2024-2025) with Camille Horbez and the OE and Entropy Seminar (2022-2023) with François le Maître. These seminars explore cutting-edge topics in group actions, orbit equivalence, and entropy theory, bringing together researchers from across the mathematical community.

Raquel Murat GarcíaView profile

Researcher

• Group Theory
• Geometry
• Topology
• +3 more

Raquel Murat García is a researcher in the Geometry, Topology, and Group Theory research group at the Mathematisches Institut of Universität Münster. Her work focuses on the interplay between topology and geometric group theory, particularly applying condensed mathematics to study group cohomology for locally compact groups. She is active in academic service as a PhD representative (2024-2025) and mentor in the university's mentoring program for female master's students. Education: Master's degree in Mathematics (2024), Bachelor's degree in Mathematics (2021). Her master's thesis explored fibrations over coset spaces, while her bachelor's thesis addressed Wiener's lemma on convolution operators. Teaching roles include co-organizing a seminar on the Boone-Higman conjecture (SS25), tutoring in Locally Compact Groups (WS24/25), and teaching assistant roles in foundational analysis courses (SS24) and number theory (WS23/24). Recent academic activities include presenting at the 2024 Profinite Rigidity Workshop in Karlsruhe and the Bielefeld-Münster Seminar on Groups, Geometry, and Topology.

Holger KammeyerView profile

Assistant Professor

• Algebraic Topology
• Profinite Groups
• Arithmetic Groups
• +3 more

Holger Kammeyer is Junior Professor for Algebra and Geometry at Heinrich Heine University Düsseldorf's Mathematical Institute, within the Faculty of Mathematics and Natural Sciences. His research focuses on algebraic topology, profinite and arithmetic groups, and ℓ²-invariants. Kammeyer's research explores profinite group properties, arithmetic group invariants, ℓ²-Betti numbers, Galois cohomology applications, and geometric methods in group theory. He develops techniques for studying profinite rigidity of lattices in Lie groups and invariants of S-arithmetic groups. Recent work includes investigations of higher rank volume profiniteness, Euler characteristics of S-arithmetic groups, bounded cohomology as a profinite invariant, and Gassmann triples with special cycle types. His publications demonstrate expertise in both theoretical developments and educational materials, including textbooks on algebraic topology and ℓ²-invariants. As Principal Investigator in multiple research initiatives, Kammeyer leads projects on geometric structures in group theory and supervises doctoral students in algebra and number theory. He organizes research events including summer schools on analytic and arithmetic groups and conferences on the interface of group theory with geometry and topology.

• Geometric Group Theory
• Profinite Rigidity
• Coxeter Groups
• +4 more

Dr. Philip Möller is a Postdoctoral Researcher at the Heinrich Heine University Düsseldorf, affiliated with the Department of Algebra and Number Theory within the Faculty of Mathematics and Natural Sciences. His research focuses on Geometric Group Theory, Profinite Rigidity, Coxeter groups, and Locally Compact Groups. He has contributed to studies on automatic continuity, graph products of groups, and the interplay between algebraic structures and geometric/topological properties. His work frequently involves collaborations with mathematicians such as Olga Varghese and Samuel M. Corson. Dr. Möller has presented his research at international conferences like the Geometric Structures in Group Theory (Oberwolfach, 2025) and the Profinite Rigidity Workshop (Karlsruhe, 2024). He has also delivered talks on topics such as Profinite Rigidity of Crystallographic Groups and Automatic Continuity for Groups in Geometric Group Theory. In teaching, he has led tutorials for courses in Algebra, Analysis, and Mathematics for Computer Science at HHU Düsseldorf and the University of Münster. His academic contributions span preprints and peer-reviewed articles in journals like Journal of Algebra and Israel Journal of Mathematics . Beyond academia, Möller is actively involved in trampolining, serving as a coach and judge. He organizes regional judging courses and contributes to licensing programs through the Westfälischer Turnerbund (WTB).

Martin BridsonView profile

Professor

• Geometric Group Theory
• Geometry of Non-Positively Curved Spaces
• Low-Dimensional Topology

Professor Martin Bridson is the President of the Clay Mathematics Institute and holds the Whitehead Professorship of Pure Mathematics at the University of Oxford's Mathematical Institute. His research spans geometric group theory, non-positively curved spaces, and low-dimensional topology, with significant contributions to understanding group presentations, profinite completions, and hyperbolic geometry. Key Affiliations: Clay Mathematics Institute (President) University of Oxford (Whitehead Professor of Pure Mathematics) Research Interests: Geometric Group Theory Geometry of Non-Positively Curved Spaces Low-Dimensional Topology Profinite Group Theory Isoperimetric Inequalities Fixed-Point Properties Scientific Awards: 2020 Steele Prize for Mathematical Exposition (with André Haefliger) Fellow of the Royal Society (2016) Fellow of the American Mathematical Society (2015) London Mathematical Society Whitehead Prize (1999)

• Group Theory
• Geometric Group Theory
• Profinite Groups
• +3 more

Nikolay Nikolov is an Associate Professor in Pure Mathematics at the Mathematical Institute, University of Oxford, where he holds a position in the Algebra research group. He earned his D.Phil from Oxford University in 2002 and maintains an active research profile in asymptotic group theory. Education: D.Phil in Mathematics, University of Oxford, 2002 Nikolov's research centers on asymptotic behavior of invariants in finite and infinite groups, with specific focus on expansion properties, word width, and growth of rank and Betti numbers. His work bridges abstract algebra and geometric structures, particularly in profinite groups and lattice theory. Recent investigations emphasize decomposition theorems and rigidity phenomena in topological group settings. Publication analysis reveals a clear trajectory toward profinite group theory, with 2024-2025 works dominated by Jordan-Holder and Krull-Schmidt theorems for profinite structures. Earlier research (2015-2019) established foundational contributions to L2-invariants, homology torsion growth, and Artin group properties, demonstrating consistent focus on group-theoretic invariants across different mathematical frameworks. Scientific Awards: Whitehead prize of the London Mathematical Society (2007) The provided information does not specify doctoral students or grant funding. Nikolov teaches Prelims Group Theory and Part C Noncommutative Rings at Oxford, contributing to both undergraduate and graduate mathematics education within the Mathematical Institute.

David McReynoldsView profile

Professor

• Geometric Group Theory
• Hyperbolic Geometry
• Topology
• +2 more

Dr. David McReynolds is the Ben McReynolds Professor of Mathematics at Purdue University specializing in geometric group theory and low-dimensional topology. His research investigates geometric structures in group theory, hyperbolic manifolds, and arithmetic lattices. Recent work focuses on homological properties of discrete subgroups in Lie groups and profinite rigidity in geometric contexts. Develops topological approaches to study group actions on symmetric spaces and geometric invariants. Advises graduate students in geometric analysis and topology. Contributes to understanding geometric structures through combinatorial and algebraic methods.