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Ciprian Manolescu is a Professor of Mathematics at Stanford University, where he joined after serving as a professor at UCLA since 2008. He holds both his undergraduate degree and doctorate from Harvard University, advised by Peter Kronheimer. His research focuses on gauge theory, low-dimensional topology, and symplectic geometry, with notable contributions to Heegaard Floer theory, Khovanov homology, and the resolution of the Triangulation Conjecture. Manolescu’s academic accolades include the 2019 E.H. Moore Research Article Prize, the 2012 European Mathematical Society Prize, and a 2004 Clay Research Fellowship. He delivered an invited lecture at the 2018 International Congress of Mathematicians and became a Fellow of the American Mathematical Society in 2017. His work bridges advanced algebraic structures with geometric problems, particularly in understanding manifold invariants and topological constraints. His teaching includes the Polya Problem Solving Seminar (Math 193) at Stanford, and he advises students competing in the Putnam Mathematics Competition. Research trends in his publications emphasize applications of Floer homology to knot theory, 4-manifold topology, and the interplay between algebraic topology and quantum field theories. Education: PhD and BA in Mathematics, Harvard University Key Research Themes: Floer homology frameworks, geometric topology, knot invariants, and manifold classification Grants & Collaborations: Involved in NSF-funded projects like the FRG: Collaborative Research: Floer Homotopy Theory (2016)

• Geometry
• Topology
• Gauge Theory
• +4 more

Steven Sivek is a Reader in Pure Mathematics at Imperial College London, affiliated with the Geometry group within the Department of Mathematics. His research focuses on contact and symplectic geometry, knot theory, gauge theory, and low-dimensional topology. He has taught courses on contact geometry, symplectic geometry, mapping class groups, and Morse theory at institutions including Imperial College London, Harvard University, and the University of Bonn. His work includes advanced topics such as Floer homology, Legendrian knots, and the interplay between contact structures and 3-manifolds. Sivek's contributions bridge geometric topology with algebraic structures, addressing questions about knot invariants, representation varieties, and topological field theories. His courses emphasize foundational texts and advanced research topics, such as the classification of tight contact structures, Morse theory applications, and symplectic fiber bundles. He has organized seminars on mapping class groups and taught graduate-level material on advanced geometry and topology. Sivek's research has been published in numerous high-impact papers, exploring themes like Khovanov homology, instanton Floer homology, and the geometry of 3- and 4-manifolds. His academic profile reflects a commitment to both teaching and cutting-edge research, with a focus on geometric and topological questions that intersect algebraic and differential structures.

• Pure Mathematics
• Topology
• Contact Geometry
• +4 more

Sungkyung Kang is a Research Fellow at the University of Oxford 's Mathematical Institute and a Stipendiary Lecturer in Applied Mathematics at Keble College (Michaelmas 2023). As a Research Associate at Keble College (2023–2024), she investigates low-dimensional topology through Heegaard Floer theory and its connections to Seiberg-Witten gauge theory. Her work focuses on knot concordance, cobordism invariants, and cabling structures. Affiliation : Mathematical Institute, University of Oxford College Roles : Stipendiary Lecturer (Keble College, Michaelmas 2023), Research Associate (Keble College, 2023–2024) Research Interests : Knot theory, 3-manifold topology, and smooth concordance problems. Her research bridges Heegaard Floer homology with gauge-theoretic invariants to analyze cobordism structures and cabling phenomena in low dimensions. Core Methods : Heegaard Floer theory Key Areas : Smooth sliceness, Torsion in concordance groups

• Knot Theory
• 3-Manifolds
• Heegaard Floer Theory
• +2 more

Frank Calegari is a Professor of Mathematics at the University of Chicago. His primary research interests include algebraic number theory, the Langlands program, Galois representations, and arithmetic geometry. He has made significant contributions to understanding reciprocity laws linking Galois representations to automorphic forms. His work often intersects with cohomology of arithmetic groups, motives, and the arithmetic of periods. Prof. Calegari has advised numerous PhD students, including Maria Stadnik, Shiva Chidambaram, and Eric Stubley. He serves on editorial boards for prestigious journals such as Algebra & Number Theory, Essential Number Theory, and the Annals of Mathematics. He actively participates in academic conferences and programs, including organizing the 2020 Arithmetic of the Langlands Program in Bonn. His research spans modularity theorems for abelian varieties, cohomology of arithmetic groups, and the study of L-functions. Key recent work includes resolving the unbounded denominators conjecture and advancing potential automorphy results over CM fields. Calegari frequently collaborates with leading mathematicians, including George Boxer, Vincent Pilloni, and Yilin Yang. He teaches advanced courses such as Honors Calculus (Math 16100) at the University of Chicago. His expository work includes lecture notes on motives and L-functions, as well as a blog compiling mathematical insights (Persiflage). Calegari’s contributions to number theory have been recognized through his editorial roles and invited lectures at institutions like the ICM and Clay Mathematics Institute.

• Algebraic Number Theory
• Langlands Programme
• Galois Representations
• +3 more

Zoltán Szabó is a Professor of Mathematics at Princeton University, affiliated with the Department of Mathematics since 2002. He holds the Henry Burchard Fine Professorship periodically. His research focuses on topology, particularly smooth 4-manifolds, Heegaard Floer homology, symplectic geometry, and knot theory. He has been recognized with prestigious awards, including the Oswald Veblen Prize in Geometry (2007) and the Packard Fellowship (1998–2003). Education: PhD from Rutgers University (1994); B.A. from Eötvös Loránd University, Budapest (1990). Professional roles include teaching courses like Topics in Knot Theory (Spring 2022) and co-developing computational tools for knot Floer homology. His work bridges geometric topology, algebraic topology, and mathematical physics, with contributions to Seiberg-Witten invariants and low-dimensional topology. Key research areas include knot theory applications, Floer homology, and geometric structures. Awards highlight his impact on theoretical mathematics. Publications span journals like Inventiones Mathematicae and Topology , with recent work on elliptic surfaces and knot lattice homology.

• Topology
• Smooth 4-manifolds
• Heegaard Floer homology
• +3 more

Miriam Kuzbary is an Assistant Professor of Mathematics at Amherst College, specializing in geometric topology and knot theory. She holds a PhD from Rice University and has held postdoctoral positions supported by the NSF. Her research explores intersections between group theory and topology, particularly in low-dimensional spaces and knot concordance. She is actively involved in organizing conferences like the Five College Geometry Topology Seminar and the Links in Dimensions 3 and 4 Conference at ICERM. Kuzbary is also committed to inclusive pedagogy, adhering to Federico Ardila’s axioms, and has received multiple teaching awards, including the Class of 1934 CIOS Honor Roll. She has advised numerous students on research projects, blending topology with interdisciplinary applications like textile structures and music theory. Educations: PhD (Rice University), MA (Rice University), BS (University of Texas at Dallas). Affiliations: Organizer of ICERM’s 2025 conference, co-founder of Atlanta Undergraduate Research Seminar. Research Interests: Focuses on link concordance, mapping class groups, and applications of topology to art/music. Utilizes Heegaard Floer homology and gauge theory. Recent work includes studies on knitted materials and Torelli group metrics. Awards: NSF Postdoctoral Fellowship, AAUW Dissertation Fellowship, NSF GRFP.

• Geometric Topology
• Low Dimensional Topology
• Knot Theory
• +4 more

Yankı Lekili is a Professor of Geometry at the Department of Mathematics, Imperial College London, affiliated with the Faculty of Natural Sciences. His research focuses on symplectic topology, low-dimensional topology, and their connections to algebraic geometry and geometric representation theory. He explores topics including mirror symmetry conjectures, Fukaya categories, and homological mirror symmetry for various geometric structures. Education: PhD in Mathematics from MIT (2009), specializing in broken Lefschetz fibrations and Heegaard-Floer homology. Teaching: Courses include Elliptic Curves, Commutative Algebra, Algebraic Topology, and Representation Theory. Research Interests: Symplectic manifolds, Lagrangian submanifolds, derived equivalences, and categorical mirror symmetry applications. His work bridges symplectic geometry with algebraic geometry, particularly through mirror symmetry. Recent studies involve Fukaya categories of singularities, noncommutative crepant resolutions, and equivariant cohomology. He collaborates internationally, contributing to topics like the Fargues-Fontaine curve and Auslander algebras.

• Symplectic Topology
• Low Dimensional Topology
• Algebraic Geometry
• +3 more

Claudius Zibrowius is a Professor of Low-Dimensional Topology at Ruhr-University Bochum's Faculty of Mathematics. He leads the Topology Group, focusing on categorified knot invariants like knot Floer homology and Khovanov homology, leveraging Fukaya categories of surfaces. His work bridges Heegaard Floer theories and quantum invariant categorifications. Current group members include postdoc Dr. Chen Zhang and PhD student Luca Marchiori. Research highlights include ERC Starting Grant (ERC-2024) and DFG funding, as well as contributions to topics like Gordian distances, Conway spheres, and mutation invariance. Notable collaborations involve Artem Kotelskiy and Liam Watson. Teaching activities include Algebraic Topology I and outreach lectures. He co-organizes conferences like 'Categorification in Low Dimensional Topology' (2025). Awards include DFG Individual Grant (2022) and ERC Starting Grant (2024). His lab engages in computational projects like kht++, a C++ program for Khovanov invariants. Beyond academia, he sings in choirs and advocates for Palestinian rights, publicly opposing Israeli-Palestinian conflict complicity.

• Low-Dimensional Topology
• Categorified Knot Invariants
• Heegaard Floer Theories
• +3 more

Matthew Edward Hedden is a Professor in the Department of Mathematics at Michigan State University's College of Natural Science, where he maintains an active research program in low-dimensional topology. His office is located in D325 Wells Hall, and he holds regular office hours via Zoom on Wednesdays and Thursdays. Hedden has established himself as a leading researcher in Heegaard Floer homology and its applications to knot theory and 4-manifold topology. Hedden's research centers on low-dimensional topology, with emphases on Heegaard Floer homology, knot concordance, and connections between symplectic topology and gauge theory. His work explores deep relationships between knot invariants, 3- and 4-manifold structures, and complex curves in Stein domains. He has made significant contributions to understanding how Floer-theoretic invariants detect geometric properties of knots and 3-manifolds, particularly through his investigations of cabling operations, satellite constructions, and concordance invariants. His research often bridges abstract topological frameworks with concrete computational techniques in knot theory. Hedden's publication record demonstrates consistent innovation in low-dimensional topology over the past two decades. His work shows a clear trajectory from foundational studies in knot Floer homology toward increasingly sophisticated applications in 4-manifold topology and connections with symplectic geometry. Key thematic developments include the systematic exploration of concordance invariants, the geometric interpretation of Floer homology through pillowcase geometry, and the extension of these techniques to study complex curves in Stein domains. His collaborative work spans multiple subfields, reflecting the interdisciplinary nature of modern geometric topology. Hedden has received significant recognition for his research, most notably the prestigious Alfred P. Sloan Research Fellowship (2011-2013). His work has been supported by multiple National Science Foundation grants, including a CAREER award. Hedden has directed substantial research funding through six National Science Foundation grants spanning 2005-2020, including the CAREER grant DMS-1150872 on Floer Homology and Low-Dimensional Topology (2012-2018) and the research grant DMS-1709016 on Floer Homology, Concordance, and Complex Curves (2017-2020). His research program has fostered numerous collaborations across the topology community, resulting in over 30 publications in top mathematics journals. Through his extensive lecture notes and resource compilations on Heegaard Floer homology, Hedden has significantly contributed to the education and training of new researchers in the field.

• Low-Dimensional Topology
• Knot Theory
• Heegaard Floer Homology
• +4 more

Robert Lipshitz is a Professor of Mathematics at the University of Oregon, specializing in low-dimensional topology and symplectic geometry. He is currently on leave for the 2025-2026 academic year to serve as the Minerva Visitor in the Mathematics Department at Princeton University, where he will deliver a series of lectures on recent techniques in low-dimensional topology. His research has significantly advanced the fields of Heegaard Floer homology and Khovanov homology, with numerous publications in top mathematics journals. Dr. Lipshitz's research primarily focuses on developing and applying bordered Heegaard Floer homology and Khovanov homology to solve problems in low-dimensional topology. His work bridges geometric topology with algebraic structures, providing powerful new invariants for studying 3- and 4-dimensional manifolds. He has made significant contributions to understanding connections between different homology theories and their applications to classical problems in knot theory and 4-dimensional topology, often combining deep geometric insights with sophisticated algebraic techniques. Dr. Lipshitz's recent publications demonstrate a consistent focus on refining and extending homological invariants in low-dimensional topology, particularly through the development of bordered techniques and stable homotopy refinements. His work shows increasing sophistication in connecting different branches of topology, with recent papers exploring applications to contact geometry, equivariant settings, and the detection of topological properties through algebraic invariants. Dr. Lipshitz has received numerous prestigious awards and fellowships supporting his research: NSF Graduate Research Fellowship NSF Mathematical Sciences Postdoctoral Research Fellowship Sloan Research Fellowship Simons Foundation Fellowship in Mathematics Multiple NSF research grants (DMS-0905796 through DMS-2505715) Dr. Lipshitz actively contributes to the mathematical community through editorial work as an editor for Quantum Topology and managing editor for Geometry & Topology. He serves as editor for chapter 3 of the K3 List, continuing Kirby's problem lists in low-dimensional topology. He has mentored numerous students, though specific names aren't listed on his website, and has developed computational tools including documentation for bfh_python, which implements algorithms for computing Heegaard Floer homology. Dr. Lipshitz is deeply involved in the topology community, frequently organizing the University of Oregon topology seminar. He has created educational resources on using Blender for mathematical illustrations and is developing tools for the mathematical community, including tutorials on creating line drawings for mathematics papers using 3D graphics software. He is also planning a conference at Princeton in Summer 2027 honoring Peter Ozsváth's 60th birthday.

• Low-dimensional topology
• Symplectic geometry
• Heegaard Floer homology
• +3 more

Jorge Becerra is a part-time Post-Doctoral Fellow at the University of Burgundy , affiliated with the Faculty of Science and working in the Mathematics-Physics team. He collaborates with Lukas Woike on quantum topology and grid homology. PhD in Mathematics from the University of Groningen. Master's degree from Utrecht University. Bachelor's degree from the University of Extremadura. His research focuses on Knot Theory , Algebraic Topology , and Category Theory , with applications in Quantum Topology and Heegaard-Floer Homology . He has co-lectured Topics in Topology at the University of Groningen and organized seminars on knot theory. He supervised D. Apol 's Bachelor's thesis on cohomology theories and contributed to teaching courses like Multivariable Analysis and Algebraic Topology . His contact email is Jorge.Becerra-Garrido@ube.fr .

• Quantum Topology
• Knot Theory
• Algebraic Topology
• +3 more

Ian Zemke is an Assistant Professor in the Department of Mathematics at the University of Oregon's College of Arts and Sciences. His research focuses on low-dimensional topology and symplectic geometry, with a particular emphasis on Heegaard Floer homology and knot theory. Education: PhD in Mathematics from University of California, Los Angeles (2017) - Advisor: Ciprian Manolescu Research Interests: Zemke's work bridges symplectic geometry and low-dimensional topology, using Heegaard Floer homology as a primary tool. His research explores fundamental questions in knot theory, 3- and 4-dimensional manifold theory, and the interplay between different Floer-theoretic invariants. Key areas include: Development of surgery formulas in Heegaard Floer homology Study of concordance and cobordism invariants for knots and links Investigation of involutive Floer homologies and their applications Analysis of exotic smooth structures on 4-manifolds Recent Research Trends: Zemke's recent publications demonstrate a concentrated focus on advancing the theoretical foundations of Heegaard Floer homology, particularly through the development of new surgery formulas and the study of involutive invariants. His work consistently addresses fundamental questions about knot concordance and the structure of 3- and 4-manifolds, with significant contributions to understanding the relationship between different Floer-theoretic invariants. Scientific Awards: Sloan Research Fellowship Funding and Support: Zemke's research is partially supported by: National Science Foundation grants DMS-1703685 and DMS-2204375 Sloan Research Fellowship Teaching and Service: Currently teaching Math 690: Morse Theory in Autumn 2025 at the University of Oregon. He maintains an active website with research materials, including Python and Sage code for computational topology, lecture notes, and slides from various conferences and summer schools.

• Low-dimensional topology
• Symplectic geometry
• Heegaard Floer homology
• +2 more

Matthew Henry Stoffregen is an Assistant Professor in the Department of Mathematics at Michigan State University (MSU). His research focuses on applying Floer theory to low-dimensional topology, with an emphasis on equivariant and homotopy-theoretic aspects of Floer homology. His work spans topics such as knot concordance, homology cobordism, and the interplay between algebraic structures and geometric topology. Stoffregen’s research interests include monopole Floer spectra, Heegaard Floer homology, and Khovanov homology. He collaborates extensively with researchers like Kristen Hendricks, Jen Hom, and Ian Zemke. Notable contributions include studies on involutive invariants, satellite knots, and the structure of homology cobordism groups. He currently advises PhD students Dean Spyropoulos, Max Throm, and Amey Joshi, and supervises postdoc Sally Collins. His research has been published in top journals such as *Geometry and Topology* and *Advances in Mathematics*. Key research themes include: Applications of Floer homology to knot theory and 3/4-manifold topology Equivariant methods in low-dimensional topology Surgery formulas and concordance obstructions His recent work explores spectral approaches to Floer theory and the classification of rationally slice knots.

• Low-Dimensional Topology
• Floer Theory
• Homotopy Theory
• +3 more

Marius Huber is a Postdoctoral Researcher at the Digital Linguistics Lab, University of Zurich, working with Prof. Lena Jäger on the SNSF-funded ProPoSaL project. His research develops topological data analysis methods for linguistic data and natural language processing applications. Education: PhD in Mathematics, Boston College (supervised by Joshua Greene) His research bridges low-dimensional topology and computational linguistics, specializing in topological data analysis, knot theory, and their applications to NLP. Current work focuses on translating abstract mathematical frameworks into practical tools for analyzing linguistic structures through persistent homology and clustering algorithms. While his foundational publications explore ribbon cobordisms in 3-manifolds, his recent trajectory demonstrates a strategic pivot toward interdisciplinary applications where topological methods solve complex problems in computational linguistics and machine learning. Dr. Huber secures research funding through the SNSF Sinergia grant for ProPoSaL and teaches graduate courses including Mathematical Foundations of Computational Linguistics (Fall 2024), Bayesian Statistics (Spring 2024), and Linear Algebra for Machine Learning (Spring 2023). He leads software development for the Digital Linguistics Lab, creating open-source topology tools including DowkerRipsComplex, DowkerComplex, AuToMATo, and SoaPy – the latter enabling computation of Heegaard Floer invariants for Seifert fibered spaces.

• Topological Data Analysis
• Low-Dimensional Topology
• Knot Theory
• +2 more

Cagatay Kutluhan is an Associate Professor at the Department of Mathematics , University at Buffalo . His research focuses on low-dimensional topology , specifically contact and symplectic geometry and gauge theory . Research Interests : Geometry and topology of 3- and 4-manifolds Equivalence of Heegaard Floer and Seiberg-Witten Floer homologies Applications of pseudo-holomorphic curves Scientific Contributions : Defined novel contact invariants using Heegaard Floer homology Proved equivalence between Heegaard Floer and Seiberg-Witten Floer theories Developed computational tools for Floer homology Grants and Support : Simons Foundation Grant #519352 NSF MSPRF #DMS-1103795 NSF Grant #DMS-1360293

• Low-dimensional topology
• Contact geometry
• Symplectic geometry
• +3 more