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Johnny Guzmán is a Professor of Applied Mathematics at Brown University, specializing in numerical analysis of partial differential equations and scientific computing. He holds a Ph.D. in Applied Mathematics from Cornell University (2005) and a B.S. in Mathematics from California State University, Long Beach (1999). His research focuses on numerical methods for PDEs, including discontinuous Galerkin methods, mixed finite element methods, and fluid-structure interaction problems. Key contributions include work on hybridizable and mixed finite element methods, discontinuous Galerkin discretizations, and stability analysis of numerical schemes. He has been funded by multiple NSF grants, including a Postdoctoral Fellowship (2005–2008) and awards totaling over $1M in research support. Notable recognitions include the Comfort and Urry Family Fund Prize (2013). Guzmán collaborates with institutions globally and serves on editorial boards for journals like Journal of Numerical Mathematics and Calcolo . His teaching spans computational linear algebra, numerical methods for differential equations, and finite element analysis.

• Numerical Analysis
• Partial Differential Equations
• Scientific Computing
• +5 more

Mark D. Haiman is a Professor at the University of California, Berkeley, Department of Mathematics, with research interests spanning algebra, combinatorics, and algebraic geometry. His work connects symmetric function theory with geometric objects like Hilbert schemes and algebraic structures such as Cherednik algebras and Hecke algebras. Appointed: 2001 Contact: mhaiman@math.berkeley.edu Teaching: Math 256B—Algebraic Geometry (Spring 2025), Math 249—Algebraic Combinatorics (Spring 2024), and others in calculus and Lie groups. Research Interests : Haiman's research focuses on Macdonald polynomials, LLT polynomials, Hilbert schemes of points in the plane, and their combinatorial and geometric implications. His work includes resolving the Macdonald positivity conjecture and the n! conjecture through algebraic geometry. Publications : Haiman has contributed to foundational papers in combinatorial and algebraic structures, including generalizations of the shuffle theorem and positivity results for LLT polynomials. His articles often bridge representation theory, symmetric functions, and geometric methods. Students : He has supervised numerous PhD students, including Magda Hlavacek (2023), Foster Tom (2022), Jeremy Meza (2021), Maryam Farahmand-Asil (2018), Maria Monks Gillespie (2016), and others working on combinatorial algebraic geometry and related fields.

• Algebra
• Combinatorics
• Algebraic Geometry
• +12 more

Brian Conrad is a Professor of Mathematics at Stanford University, specializing in number theory and arithmetic geometry. He holds a position in the Department of Mathematics and has contributed extensively to algebraic geometry, algebraic number theory, and representation theory. His research encompasses foundational work on reductive groups, pseudo-reductive groups, and their applications in arithmetic contexts. Dr. Conrad is an editor for the Journal of the AMS, Algebra and Number Theory, and IMRN. He has organized numerous learning seminars, including those on étale cohomology and the BSD conjecture, and has taught advanced courses on algebraic geometry, class field theory, and modular forms. His work bridges classical algebraic geometry with modern arithmetic applications, emphasizing foundational proofs and geometric intuition. His editorial roles and seminar leadership reflect his commitment to advancing mathematical exposition and education. Education details are not explicitly provided in the texts, but his academic trajectory includes significant contributions to the field through publications and mentorship. Dr. Conrad's research has led to advancements in areas such as the classification of algebraic groups, étale cohomology, and the arithmetic of elliptic curves. His collaborative work with mathematicians like Chai, Oort, and Prasad has produced influential monographs, including Pseudo-reductive Groups and Complex Multiplication and Lifting Problems .

• Number Theory
• Arithmetic Geometry
• Algebraic Geometry
• +3 more

Dima Arinkin is a Professor in the Department of Mathematics at the University of Wisconsin–Madison, specializing in algebraic geometry with significant contributions to geometric representation theory and mathematical physics. His research focuses on: Geometric Langlands Program: Developing frameworks connecting automorphic forms and Galois representations through geometric methods Moduli Spaces: Analyzing spaces of algebraic connections, Higgs bundles, and their compactifications D-modules: Studying systems of linear differential equations via algebraic geometry Integrable Systems: Investigating geometric structures in soliton theory and Painlevé equations Irregular Singularities: Exploring connections with irregular behavior on algebraic curves Analysis of his publications (2008-2016) reveals consistent advancement in geometric Langlands through derived algebraic geometry techniques, particularly in relating singular support of sheaves to automorphic forms and establishing oper structures for connections. No scientific awards are documented in the provided materials. No information regarding student advisement or research grants appears in the source texts.

• Algebraic Geometry
• Geometric Langlands Program
• Moduli Spaces
• +3 more

Sheldon Katz is a Professor of Mathematics at the University of Illinois at Urbana-Champaign (UIUC), with a joint appointment in the Department of Physics. He holds a Ph.D. in Mathematics from Princeton University (1980) and a B.S. from MIT (1976). Previously, he was a Regents Professor of Mathematics at Oklahoma State University before joining UIUC in 2001. Katz's research focuses on algebraic geometry and mathematical physics, particularly string theory and supersymmetric quantum field theories. His work bridges geometry and physics, exploring topics like Gromov-Witten theory, toric varieties, and F-theory. He co-authored the influential book Mirror Symmetry and Algebraic Geometry (1999), a cornerstone in the field. His recent research includes studies on BPS invariants, Calabi-Yau manifolds, and topological string theory. Key contributions include analyses of F-theory, mirror symmetry, and geometric dualities in string compactifications. He teaches advanced courses in algebraic geometry and mathematical physics at UIUC. While no explicit awards are listed, his extensive publication record and academic leadership reflect significant contributions to the field. Katz’s work continues to explore the interplay between algebraic geometry and fundamental physics.

• Algebraic Geometry
• Mathematical Physics
• String Theory
• +3 more

Jack Huizenga is an Associate Professor in the Department of Mathematics at The Pennsylvania State University. His research focuses on algebraic geometry, particularly Hilbert schemes of points, moduli spaces of vector bundles, and interpolation problems. He is a co-organizer of the Algebra and Number Theory Seminar at Penn State. Education: Ph.D., Harvard University (2012). He has designed courses introducing algebraic geometry through linear algebra and interpolation problems, such as Polynomial Interpolation: An Introduction to Algebraic Geometry . Research Interests: Algebraic Geometry, with a focus on Brill-Noether theory, moduli spaces, vector bundles on surfaces, and birational geometry. His work explores geometric structures like Hilbert schemes, projective plane blowups, and stability conditions of sheaves. Publications highlight advanced topics in algebraic geometry, including cohomology of vector bundles, Seshadri constants, and geometric interpolation problems. He has collaborated extensively with researchers like Izzet Coskun on foundational problems in moduli spaces and stability conditions. No scientific awards are explicitly listed in the provided information. His advising and grant activities are not detailed here, though he has authored lecture notes and exercises for specialized courses. He maintains a research website at https://sites.psu.edu/jhuizenga/ .

• Algebraic Geometry
• Moduli Spaces
• Hilbert Schemes
• +3 more

Bianca Viray is a Professor in the Department of Mathematics at the University of Washington. Her research focuses on arithmetic geometry, number theory, and algebraic geometry, particularly exploring rational points on varieties and Brauer-Manin obstructions. She actively organizes the UW Number Theory Seminar and collaborates on projects addressing the distribution of mathematical potential and inclusive education. Viray's work bridges theoretical advancements with pedagogical contributions, including workshops on effective mathematical communication and resources for academic success. Her research interests emphasize the intersection of arithmetic and algebraic geometry, with a focus on quadratic points, conic bundles, and the persistence of obstructions in rationality questions. She has contributed to foundational studies on Brauer groups, del Pezzo surfaces, and the arithmetic of curves, often involving collaborations on computational algebraic geometry tools like Magma and Sage. Viray's articles span topics like quartic del Pezzo surfaces, parameterized points on curves, and number fields generated by linear systems. She advocates for equitable mathematics education through initiatives rooted in Federico Ardila’s axioms, emphasizing dignity and accessibility in academic environments.

• Arithmetic Geometry
• Number Theory
• Algebraic Geometry
• +3 more

Chris Monico is an Associate Professor in the Department of Mathematics & Statistics at Texas Tech University . He has been a faculty member there since 2003, following post-doctoral research at the University of Notre Dame. Education B.S. in Mathematics – Monmouth University M.S. in Mathematics – University of Notre Dame Ph.D. in Mathematics – University of Notre Dame Research Focus Monico’s scholarship centers on the intersection of cryptology , computational algebra , and number theory . A significant recent thrust has been the application of machine-learning techniques to mathematical finance , evidenced by work on random-forest models for option pricing and high-frequency trading risk metrics. Parallel lines of inquiry include post-quantum cryptographic schemes built on tropical algebra and semigroup actions, as well as classical problems in Ramsey theory and combinatorial semigroups . Publication Trends Between 2015 and 2025 Monico has published prolifically, with a clear shift around 2020 toward mathematical finance and machine-learning applications , alongside continued output in algebraic cryptanalysis and combinatorics . His 2024–2025 articles emphasize data-driven models in trading, whereas 2020–2021 works concentrate on cryptanalyses of tropical and group-based key-exchange systems. Earlier contributions focus on computational number theory and semigroup-based cryptography. Contact Information Email: c.monico@ttu.edu Phone: 806-834-4144 Office: Department of Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409-1042 Advising & Grants No specific doctoral or master’s students, funded grants, or named awards are detailed in the provided text. Laboratory or Research Group The text does not mention any dedicated laboratory or research group.

• Cryptology
• Computational Algebra
• Number Theory
• +6 more

Dori Bejleri is an Assistant Professor in the Department of Mathematics at the University of Maryland, College Park. Prior to this, he was a Benjamin Peirce and NSF postdoctoral fellow at Harvard University (2019–2023) and an NSF postdoctoral fellow at MIT (2018–2019). He earned his PhD in 2018 from Brown University under Dan Abramovich's supervision. His research focuses on algebraic geometry, particularly moduli spaces and birational geometry, with connections to number theory, enumerative geometry, combinatorics, and geometric representation theory. His work is supported by NSF grant DMS-2401483. He has organized several academic events, including the JHU-UMD Algebra and Number Theory Day (2024) and the Perspectives on Moduli in Algebraic Geometry conference (2025). Bejleri has taught graduate courses such as Rationality Questions in Algebraic Geometry (Spring 2022), Birational Geometry of Algebraic Varieties (Fall 2020), and Moduli Spaces in Algebraic Geometry (Fall 2019). His research spans topics like wall-crossing phenomena in moduli spaces, compactifications of elliptic surfaces, and motivic Hilbert zeta functions. He has also contributed to the study of stable log pairs and geometric representation theory. His teaching and research reflect a commitment to advancing foundational questions in algebraic geometry while engaging with interdisciplinary connections. His academic contributions include organizing seminars and mentoring students through advanced topics in geometry and topology.

• Algebraic Geometry
• Moduli Spaces
• Birational Geometry
• +3 more

Alexander S. Merkurjev is a Professor of Mathematics at the Department of Mathematics, University of California, Los Angeles (UCLA). He specializes in algebraic K-theory, Galois cohomology, quadratic forms, and cohomological invariants of algebraic groups. His work bridges algebraic geometry, number theory, and representation theory. Research interests include: algebraic groups, motivic cohomology, essential dimension, degenerate Massey products, and rationality problems of classifying spaces. He investigates questions related to Galois representations, invariants of algebraic structures, and geometric aspects of algebraic K-theory. Recent work focuses on Massey vanishing conjectures, cohomological invariants of spinor groups, and p-adic Galois representation theory. His 2025 papers address advanced topics in non-Abelian cohomology and lifting problems, while 2023-2024 publications explore fourfold Massey products and connective K-theory operations. Earlier contributions include foundational work on essential dimension and cohomological invariants of algebraic tori. His research has been published in leading mathematics journals and includes collaborations with top specialists in algebraic geometry and number theory. Notable results include the proof of Suslin's conjecture on reduced Whitehead groups and the establishment of cohomological frameworks for studying algebraic groups.

• Algebraic Groups
• Algebraic K-Theory
• Galois Cohomology
• +4 more

Erik Carlsson is a Professor in the Mathematics department at the University of California, Davis. His research spans multiple areas of pure and applied mathematics, connecting deep theoretical concepts with practical computational applications. He received his Ph.D. from Princeton University under Professor Andrei Okounkov in 2008, and a B.S. in Mathematics with honors and a minor in Computer Science from Stanford University in 2003. Carlsson's research focuses on representation theory, algebraic geometry, algebraic combinatorics, computational topology, and connections with nonconvex optimization. He is particularly interested in connections between Goresky-Kottwitz-Macpherson (GKM) spaces and applications to Macdonald theory and combinatorics. His work also includes computational topology, especially persistent homology, which he develops in collaboration with John Carlsson. One of his recent developments is a method for constructing the alpha complex in high dimension using the powerful duality principle in mathematical optimization. His recent publications show a clear trend toward bridging theoretical mathematics with computational applications. His work spans from proving deep conjectures in algebraic combinatorics (like the shuffle conjecture) to developing practical algorithms for topological data analysis. The interdisciplinary nature of his work connects pure mathematical theory with applications in data science, computer vision, and optimization problems. Carlsson has made significant contributions to multiple fields of mathematics through his collaborations and independent work. His research has implications for both theoretical mathematics and practical computational problems, with recent publications as of 2024 demonstrating his continued active research program.

• representation theory
• algebraic geometry
• algebraic combinatorics
• +5 more

Maxim L. Yattselev is a Professor in the Department of Mathematical Sciences at Indiana University–Purdue University Indianapolis (IUPUI) . He has held prior positions as a Visiting Assistant Professor at the University of Oregon and a Visiting Scholar at Vanderbilt University. Education: Ph.D. and M.S. in Mathematics from Vanderbilt University (2007, 2004), M.S. and B.S. from Dnepropetrovsk National University (2001, 2000). Research Interests focus on meromorphic approximation, orthogonal polynomials, integrable systems, random polynomials, and spectral theory. He explores connections between these areas and applications to Painlevé equations, random matrix theory, and convergence of rational approximants. Publications highlight advancements in strong asymptotics for Angelesco systems, spectral theory of Jacobi matrices on trees, universality in random polynomial roots, and convergence properties of Padé and Hermite–Padé approximants. His work often employs Riemann–Hilbert techniques and potential theory. Advising: Mentored Ph.D. students Hanan Aljubran and Ahmad Barhoumi on random polynomials and multiple orthogonal polynomials. Teaching includes advanced courses in complex analysis, real analysis, orthogonal polynomials, and differential equations at IUPUI, University of Oregon, and Vanderbilt University.

• Meromorphic Approximation
• Orthogonal Polynomials
• Integrable Systems
• +3 more

Maksym Fedorchuk is a Professor in the Department of Mathematics at Boston College. He holds a S.B. from MIT and a Ph.D. from Harvard University. His research focuses on algebraic geometry, particularly moduli problems and geometric invariant theory (GIT). He has contributed significantly to the Hassett-Keel program, exploring log canonical models of moduli spaces of curves, and has studied GIT stability of syzygies and Hilbert points of curves. His work often involves collaborations on topics like moduli spaces of weighted stable curves, Fano varieties, and the geometry of canonical curves. Key research themes include stability conditions in GIT, log minimal model programs for moduli spaces, and the interplay between algebraic geometry and combinatorial structures. Fedorchuk has published extensively in top journals such as Inventiones mathematicae , Compositio Mathematica , and Duke Math. J. . His recent work addresses K-moduli of Fano varieties and the symmetric F-conjecture. He has also developed computational tools, including a Macaulay2 package for analyzing direct sum decomposability of polynomials. Professional activities include organizing workshops such as AGNES@BC 2024 and maintaining an active research page with preprints and lecture notes. His contributions bridge foundational theory with computational methods, influencing both pure algebraic geometry and adjacent fields like quantum information through moduli of qubit states.

• Algebraic Geometry
• Moduli Theory
• Geometric Invariant Theory (GIT)
• +3 more

Matt Hogancamp is an Assistant Professor in the Department of Mathematics at Northeastern University. His research focuses on advanced areas of topology and algebra, particularly knot homology theories, categorification, and geometric representation theory. He is affiliated with Northeastern University's Mathematics department and maintains an office in Lake Hall. His work bridges algebraic structures like Soergel bimodules with topological invariants such as Khovanov-Rozansky homology. Research Interests: Knot Homology & Link Invariants Categorification of Quantum Groups Soergel Bimodules & Representation Theory Low-Dimensional Topology Algebraic Structures in Topology Recent Work Trends: His publications emphasize categorification techniques applied to knot theory and representation theory, with notable contributions to sl2 homology, Khovanov-Rozansky theories, and geometric constructions involving Hilbert schemes and Fukaya categories. The 2024-2025 papers highlight advancements in colored homology, annular invariants, and deformation techniques. No scientific awards are listed in the provided materials. His advising record and grant details are not specified in the current data. He is associated with research groups and projects exploring topological quantum field theories and diagrammatic algebra.

• Knot Homology
• Categorification
• Geometric Representation Theory
• +3 more

Juan Migliore is a Professor in the Department of Mathematics at the University of Notre Dame. His research focuses on Algebraic Geometry and Commutative Algebra, particularly liaison theory, Hilbert functions, and the Weak Lefschetz Property. He holds a B.A. from Haverford College (1978) and a Ph.D. from Brown University (1983). He has authored influential works, including the book 'Introduction to Liaison Theory and Deficiency Modules' (1998) and co-authored key papers on topics like Gorenstein liaison and monomial ideals. His teaching includes courses such as Introduction to Algebraic Geometry (Spring 2025). Professor Migliore has been actively involved in academic seminars and international workshops, contributing to the field through collaborative research and mentorship. His work bridges algebraic structures and geometric insights, reflecting a deep engagement with foundational problems in his disciplines.

• Algebraic Geometry
• Commutative Algebra
• Liaison Theory
• +3 more