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Clara LöhView profile

Professor

• Simplicial Volume
• Bounded Cohomology
• L^1-Homology
• +3 more

Prof. Dr. Clara Löh is a Professor at the University of Regensburg's Faculty of Mathematics. Her research focuses on geometric topology, bounded cohomology, simplicial volume, and computational methods in mathematics. She leads multiple research projects funded by SFB 1085 (Higher Invariants) and GRK 1692 (Curvature, Cycles, and Cohomology). Her research interests include: Simplicial volume and its applications in manifold theory L^2-invariants and their connections to geometric group theory Computability aspects in geometric topology Development of proof assistants for mathematical verification Her publications demonstrate a consistent focus on homotopy theory, K-theory, and equivariant topology, with recent work exploring rigid structures in algebraic K-theory and spectral classifications. Dr. Löh currently advises several PhD students and postdoctoral researchers, and has mentored numerous doctoral candidates to completion. She serves on editorial boards for Forum Mathematicum and Indagationes Mathematicae.

Sergey FominView profile

Professor

• Combinatorics
• Algebra
• Geometry
• +4 more

Sergey Fomin is the Richard P. Stanley Distinguished University Professor in the Department of Mathematics at the University of Michigan. His research focuses on combinatorics and its applications in algebra, geometry, and other mathematical domains, with significant contributions to cluster algebras, incidence geometry, and real algebraic curves. He holds a Ph.D. from St. Petersburg State University (1982). His work bridges foundational combinatorial structures with advanced algebraic and geometric theories. Education: Ph.D., St. Petersburg State University (1982) Research Interests: Combinatorics, algebra, geometry, and their interplay. Key areas include cluster algebras, incidence geometry, distance geometry, and real algebraic curves. His recent work emphasizes combinatorial approaches to algebraic structures and geometric problems. Publications Trends: Fomin’s articles span combinatorial algebra, geometric structures, and cluster theory. Recent works explore cyclic quivers, tilings, mutation cycles, and Heronian friezes, reflecting a focus on structural patterns and their applications. Labs/Teams: None explicitly mentioned, though his research often involves collaborations in algebraic combinatorics and geometry.

Vin de SilvaView profile

Professor

• Applied Algebraic Topology
• Machine Learning
• Sensor Networks
• +3 more

Vin de Silva is a Professor of Mathematics and Statistics at Pomona College, part of The Claremont Colleges, since 2005. His work focuses on applying geometry and topology to data analysis, sensor networks, and machine learning. He holds a D.Phil. from Oxford University and a Master of Arts from Cambridge University. Research interests include Applied Algebraic Topology, Machine Learning, and Topological Data Analysis. His notable contributions span persistent homology, sensor network coverage, and tensor decomposition. He has collaborated with leading researchers like Robert Ghrist and Gunnar Carlsson. Recent publications include work on Zigzag Persistent Homology (2009), sensor network algorithms (2007), and tensor rank analysis (2008). His research emphasizes geometric insights in interdisciplinary problems. Awards: 2012: Pomona College Wig Distinguished Professor Award for Excellence in Teaching 2007: Scientific American SciAm 50 Award for sensor network coverage algorithms Teaches courses like Combinatorics, Differential Equations/Modeling, and Topics in Geometry and Topology. His grants and lab activities focus on computational topology and data science applications.

Ariane CarranceView profile

Researcher

• Combinatorics
• Probability Theory
• Discrete Metric Spaces
• +5 more

Ariane Carrance is a postdoctoral researcher at the Department of Mathematics, Faculty of Mathematics, University of Vienna, where she works with Professor Nathanaël Berestycki. Her research program bridges combinatorics, probability theory, and theoretical physics with applications to quantum gravity. PhD in Mathematics, Institut Camille Jordan, supervised by Grégory Miermont and Fabien Vignes-Tourneret Postdoctoral position at Laboratoire de Mathématiques d'Orsay with Nicolas Curien and Jean-François Le Gall Hadamard lecturer at Centre de Mathématiques Appliquées de l'École polytechnique Dr. Carrance specializes in the combinatorial and probabilistic aspects of discrete metric spaces. Her work in dimension 2 focuses on specific families of maps, while in higher dimensions she investigates "colored trisps" and associated tensor models. She has made significant contributions to the understanding of random discrete structures and their continuum limits, with implications for quantum gravity theories. Her research combines deep theoretical insights with computational approaches, including development of mathematical software. Dr. Carrance's publication record demonstrates a consistent progression from foundational work on planar maps and triangulations toward more complex higher-dimensional structures. Her recent work shows increasing sophistication in handling the interplay between combinatorial structures and probabilistic phenomena, with particular attention to asymptotic behaviors and scaling limits. The mathematical tools she employs span from classical combinatorics to advanced probability theory and computational mathematics. Dr. Carrance has collaborated with leading researchers in probability theory including Nicolas Curien, Jean-François Le Gall, and Nathanaël Berestycki. She co-developed the SageMath package dynpuiseux for Puiseux series expansions, demonstrating her commitment to computational approaches in pure mathematics. Her research is supported through postdoctoral fellowships and academic positions at prestigious institutions across Europe. As a member of the probability research group at the University of Vienna, Dr. Carrance contributes to a vibrant mathematical community focused on stochastic processes, random geometry, and their applications. Her work connects with broader efforts to understand the mathematical foundations of quantum gravity through discrete approaches.