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Dirk HachenbergerView profile

Associate Professor

• Discrete Mathematics
• Finite Fields
• Coding Theory
• +6 more

Prof. Dr. Dirk Hachenberger is an Associate Professor of Mathematics for Computer Scientists at the University of Augsburg, Germany. He is affiliated with the Faculty of Mathematics, Natural Sciences and Technology, specifically within the Institute of Mathematics where he works in the Chair of Discrete Mathematics, Optimization and Operations Research. His academic work focuses on theoretical and applied aspects of discrete structures, with particular emphasis on finite fields and their applications in coding theory and cryptography. Prof. Hachenberger's research interests span multiple areas of discrete mathematics, with a strong focus on finite fields , normal bases , and completely free elements . His work demonstrates deep connections between pure algebra and practical applications in information security. He has made significant contributions to understanding primitive elements in field extensions and developing theoretical frameworks for various algebraic structures used in cryptographic systems and error-correcting codes. Analysis of Prof. Hachenberger's publication record reveals a consistent focus on algebraic structures with applications in information theory. His work shows a progression from foundational theoretical research on normal bases to more applied studies on coding theory, demonstrating both mathematical depth and practical relevance. The recurring themes in his research include primitive elements, field extensions, and algebraic structures with cryptographic applications. Among his notable recognitions is the Prize for Good Teaching awarded by the Bavarian State Minister for Science, Research and the Arts in 2004, highlighting his excellence in academic instruction. Prof. Hachenberger has supervised numerous graduate students, with thesis records spanning from 2006 to 2022. His supervision covers both theoretical mathematical investigations and applied business mathematics problems, reflecting the interdisciplinary nature of his work. He has also authored influential textbooks including "Mathematik für Informatiker" (2005, 2008) and "Topics in Galois Fields" (2020), which have significantly contributed to mathematical education for computer scientists.

Jiuya WangView profile

Assistant Professor

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

Jiuya Wang is an Assistant Professor in the Department of Mathematics at the University of Georgia. His research lies at the intersection of algebraic and analytic number theory , focusing on problems related to Malle's conjecture , class group statistics , and Galois theory . Previously, he was a Phillip Griffiths Research Assistant Professor at Duke University and completed his PhD at the University of Wisconsin-Madison under the supervision of Melanie Matchett Wood. Education: PhD in Mathematics, University of Wisconsin-Madison (2018) Research Interests: Wang's work spans algebraic number theory and arithmetic geometry , with a particular emphasis on: Counting number fields and their asymptotic distributions Class group torsion and Cohen-Lenstra-Martinet heuristics Galois representations and their applications to conjectures like Brumer-Stark Energy minimization and potential theory in analysis Publications Overview: His recent publications (2020-2023) cover a broad spectrum including counterexamples to conjectures, improved bounds for field counts, sharp inequalities in analysis, and advanced algebraic structures. Notable works include proving cases of Malle's conjecture , establishing pointwise bounds for ℓ-torsion , and resolving the sharp Erdős-Turán inequality . Teaching & Mentorship: Current Courses: Math 2250 (Fall 2022) Previous Courses: Math 3000, Math 3300 (UGA), Math 401, Math 212 (Duke), Math 234 (UW-Madison) Student Mentorship: Co-led undergraduate research (DoMath at Duke, 2020) Organizational Roles: Organizer, Spring 2022 reading seminar on algebraic number theory (UGA) Co-organizer, AMS special session on counting methods (2019)

• Algebraic K-theory
• Algebraic Number Theory
• Algebraic Geometry
• +3 more

Prof. Oliver Bräunling is a full professor at the Department of Mathematics, Albert-Ludwigs-Universität Freiburg, leading the Chair of Algebra and Geometry (Lehrstuhl für Algebra und Geometrie). His research focuses on algebraic K-theory, algebraic number theory, and representation theory, with significant contributions to homological algebra and category theory. He earned his PhD in Mathematics from the same university in 2012 and completed his habilitation in 2018. Bräunling actively advises three PhD students: Julius Giesler, Lennart Gehrmann, and Tobias Columbus. He received the prestigious DFG Heisenberg Fellowship in 2022. His research explores intricate connections between algebraic structures and geometric/topological concepts, with recent work emphasizing derived categories, model categories, and Langlands program aspects. Over 15 key publications from 2009–2023 reflect his expertise in advanced algebraic methodologies. Bräunling teaches graduate courses in algebra and co-organizes the university's algebra seminar. He collaborates with international research networks and serves on editorial boards for specialized journals.

Paul TrumanView profile

Senior Lecturer

• Algebraic Number Theory
• Hopf-Galois Theory
• Skew Braces
• +2 more

Dr. Paul Truman is Senior Lecturer in Mathematics at Keele University, specializing in algebraic number theory and Hopf-Galois theory. His research advances structural relationships between skew braces and Hopf-Galois structures on field extensions. He co-authored the monograph 'Hopf algebras and Galois module theory' (AMS 2021) and maintains the international conference series on Hopf algebras. Current projects investigate generalized algebraic structures corresponding to non-normal field extensions.

Mikhail KotchetovView profile

Professor

• Hopf Algebras
• Lie Theory
• Noncommutative Ring Theory
• +2 more

Mikhail Kotchetov is a Professor in the Department of Mathematics and Statistics at Memorial University, Canada. He holds a Cand.Sc. (2003) and M.Sc. (1998) from Moscow State University (Lomonosov) and a Ph.D. (2002) from Memorial University. After postdoctoral positions in Saskatoon, Ottawa, and Los Angeles (2002–2005), and a teaching role at DePaul University, he joined Memorial University in 2006. His research centers on Hopf algebras , Lie theory , and noncommutative ring theory , with applications in knot theory, quantum physics, and statistical mechanics. Key themes include: Group gradings on algebras (Lie, Jordan, associative) Structure and classification of graded-division algebras Connections to real forms of classical Lie algebras His publications (2015–2023) predominantly explore algebraic structures, graded modules, superalgebras, and classification problems. No scientific awards or student advisees are listed. He is affiliated with the Atlantic Algebra Centre and teaches courses in Linear Algebra, Group Theory, and Galois Theory.

Jens Carsten JantzenView profile

Professor

• Algebraic Groups
• Lie Algebras
• Representation Theory

Jens Carsten Jantzen is a Professor of Mathematics at Aarhus Universitet , Denmark. Born in Störtewerkerkoog, Germany on October 18, 1948, he has held academic positions at prestigious institutions including the University of Oregon, Universität Hamburg, and Universität Bonn. His career spans over four decades with significant contributions to algebraic groups, Lie algebras, and representation theory. Current: Professor at Aarhus Universitet (1995–present) Previous: University of Oregon (1988–1995), Universität Hamburg (1985–1988), Universität Bonn (1978–1985) Jantzen’s research focuses on Algebraic Groups , Lie Algebras , and Representation Theory , with particular emphasis on modular representations, cohomology, and nilpotent orbits. His publications demonstrate a deep exploration of quantum groups, highest weight modules, and geometric methods in representation theory. He has served on editorial boards for leading journals such as Representation Theory and Acta mathematica . Notable awards include the Felix-Hausdorff-Gedächtnispreis (1975) , Fellow of the American Mathematical Society (2011) , and Member of the Academia Europaea (2012) .

Georgios PappasView profile

Professor

• Number Theory
• Algebraic Geometry
• Representation Theory
• +7 more

Georgios Pappas is a Professor in the Department of Mathematics at Michigan State University (MSU), located in Wells Hall. He is part of the College of Natural Science. His research spans several areas including number theory, algebraic geometry, representation theory, and arithmetic algebraic geometry. Additionally, his recent work explores gamification in education, environmental sustainability, and autonomous vehicle technology. Research Interests: Pappas' primary focus includes number theory, algebraic geometry, and representation theory, with a concentration on arithmetic algebraic geometry. His foundational work addresses Shimura varieties, Galois module structures, and Riemann-Roch theorems. Recently, he has expanded into interdisciplinary fields such as gamified educational tools, metaverse frameworks for waste management, and ethical implications of automated vehicles. Publications: His notable contributions include foundational research on Shimura varieties and their reductions modulo primes, alongside recent publications on gamified virtual libraries, drone simulators for search-and-rescue, and ethical considerations for autonomous systems. These works highlight his dual expertise in pure mathematics and applied technological innovation. Advising & Grants: No specific grants or advising details are provided in the text. His work appears to be primarily research-driven with a focus on collaborative interdisciplinary projects. Labs & Teams: No affiliated labs or teams are explicitly mentioned, though his publications suggest involvement in cross-disciplinary initiatives at MSU.

Jang-Heon OhView profile

Professor

• Algebraic Number Theory
• Iwasawa Theory
• Elliptic Curves

Jang-Heon Oh is a Professor in the Department of Mathematics and Statistics at Sejong University, South Korea, specializing in advanced theoretical mathematics with a focus on number theory and algebraic structures. His educational foundation includes: Ph.D. from Ohio State University (1995) M.S. from Seoul National University (1987) B.S. from Seoul National University (1985) Professor Oh's research centers on Algebraic Number Theory , Iwasawa Theory , and Elliptic Curves , with seminal contributions to the computation of Iwasawa invariants, construction of anti-cyclotomic extensions, and relationships between Zeta functions and Iwasawa modules. His work bridges abstract algebra with deep arithmetic insights, particularly in the context of Galois representations and class field theory. Analysis of his publication timeline reveals sustained expertise in p-adic methods and modular arithmetic, with recent works (2021-2022) advancing structural understanding of Zp-extensions and Iwasawa modules. His research consistently addresses foundational questions in number theory, demonstrating exceptional longevity and depth in exploring connections between algebraic invariants and analytic functions. While no specific advising relationships or grant details appear in the source material, his h-index of 16 and 14 total publications since 1998 reflect significant scholarly influence. His professional trajectory includes postdoctoral appointments at KIAS (1996-2000) and MPIM Bonn (2001-2002), establishing a robust international research profile.

• Discrete Mathematics
• Number Theory
• Algebraic Geometry
• +10 more

Professor Gary McGuire is a Full Professor in the School of Mathematics and Statistics at University College Dublin (UCD), specializing in discrete mathematics, number theory, algebraic geometry, and cryptography. He holds a PhD from the California Institute of Technology and has been a central figure in advancing research in finite fields and their applications. BSc, University College Dublin MSc, University College Dublin PhD, California Institute of Technology His research focuses on algebraic structures over finite fields, including Galois theory, permutation polynomials, error-correcting codes, and quantum codes. He has made significant contributions to the understanding of supersingular curves, L-polynomials, and lattice-based cryptanalysis. His work spans theoretical advances and practical applications in cryptography and computational mathematics. The recent publications reflect a strong trend in algebraic and computational number theory, with emphasis on Galois groups of linearized polynomials, quantum code construction, and discrete logarithm algorithms. His work often involves deep connections between algebraic geometry and coding theory, particularly in the construction of MDS and quantum codes from generalized monomial-Cartesian and algebraic geometry codes. Notable scientific awards and recognitions include: Best Paper Award at CRYPTO 2013 Invited Speaker at the 12th International Conference on Finite Fields (2015) Invited Speaker at the 25th British Combinatorial Conference (2015) Invited Session Speaker at the AAAS Annual Meeting (2014) Speaker at multiple international workshops on finite fields, cryptography, and polynomials Professor McGuire actively supervises PhD students and has coordinated key modules such as Galois Theory, Cryptography, and Numbers & Functions. He has secured research grants, including one on the simulation of photo-electronic excitation in nanofilms. His most famous contribution is the proof that no 16-clue Sudoku puzzle exists, achieved through a novel hitting set enumeration algorithm. He is a principal investigator in computational and theoretical mathematics with ongoing collaborations across Europe. He is a member of research teams focused on finite field applications, cryptographic protocols, and algebraic coding theory. His lab-like collaborative environment involves work with postdocs and researchers on projects related to discrete logarithm computation, polynomial factorization, and quantum code design.

Shrawan KumarView profile

Professor

• Representation Theory
• Algebraic Geometry
• Lie Algebras
• +5 more

Shrawan Kumar is the J.R. & L.S. Parker Distinguished Professor in the Department of Mathematics at the University of North Carolina at Chapel Hill. He joined UNC in 1991 and has held the distinguished professorship since 2010. Additionally, he maintains an adjunct position at the Tata Institute of Fundamental Research (2006–present). His academic journey includes a B.Sc. from Gorakhpur University (1973), an M.Sc. from Bombay University (1975), and a Ph.D. from Bombay University (1986) under the supervision of S. Ramanan. Kumar's research centers on representation theory, algebraic geometry, and topology, with a focus on semisimple groups, Kac-Moody algebras, and their flag varieties. He investigates moduli spaces of principal bundles, eigenvalue problems, and geometric structures in representation theory. Key areas include Frobenius splitting, tensor product decompositions, and conformal blocks, blending algebraic, geometric, and combinatorial methods. His recent publications (2020–2025) demonstrate sustained engagement with representation theory, Kac-Moody algebras, and algebraic geometry. Trends include advances in equivariant K-theory, conformal field theory generalizations, combinatorial counterexamples, and homological structures in Lie theory. Works frequently intersect mathematical physics, showcasing applications in quantum algebra and vertex operator algebras.

• Algebraic Geometry
• Commutative Algebra
• Homological Algebra
• +7 more

Rosanna Utano is an Associate Professor of Algebra in the Department of Mathematics at the Faculty of Sciences, University of Messina. She has been a confirmed associate professor for the scientific-disciplinary sector MAT02 Algebra since October 1, 2001. Her academic career includes significant leadership roles such as serving as President of the Degree Course in Mathematics and of the Specialist Degree Course in Mathematics at the University of Messina from 2004 to 2007, and as Orientation Delegate for the Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences from 2015 to 2018. Dr. Utano received her degree in Mathematics (general major) from the University of Messina in 1980 with highest honors (110/110 cum laude), and completed her PhD in Mathematics in 1988 with a thesis entitled "Complete Intersections and Finite Universal Modulus of Differentials." Her educational background also includes a high school diploma in science earned in 1976 with a perfect score of 60/60. Her research focuses on Algebraic Geometry, Commutative Algebra, Homological Algebra, and Algebraic Combinatorics, with particular emphasis on numerical semigroups and generalized numerical semigroups. Her work explores Jacobian criteria for regularity, resolutions of singularities, derivations of rings, symmetric algebras of finitely generated modules, Hilbert functions, Betti numbers, and the Eisenbud-Goto conjecture. Dr. Utano has made significant contributions to the understanding of symmetric and Rees algebras of finitely generated modules and their invariants, as well as binomial ideals associated with polyominoes. Dr. Utano's publication record demonstrates a consistent research trajectory in algebraic structures, with recent work focusing on numerical semigroups, polyomino ideals, and symmetric algebras. Her most recent publications (2022-2024) explore the geometry of blowing-ups of quadrics, Gröbner bases of polyominoes, and properties of numerical semigroups. Earlier works examined Rees algebras, syzygy modules, and generalizations of Wilf's conjecture. Member of the Scientific Committee of the Interdisciplinary Series "Algebra and its Applications: Between Classical and Modern", Aracne Member of section no. 3 of the GNSAGA of INDAM with the qualification of researcher Member of the UMI (Italian Mathematical Union) Member of the EMS (European Mathematical Society) Member of the SIMAI (Italian Society of Applied and Industrial Mathematics) Associate member of the Accademia Peloritana dei Pericolanti of Messina Dr. Utano has supervised over eighty graduate theses on topics in Algebra and Geometry and served as supervisor for three PhD theses in Mathematics. She has received funding for research projects including a type A research grant for "Numerical semigroups, generalized numerical semigroups and affine semigroups: theoretical and computational aspects" (2022-present). She has also directed numerous research projects and hosted international collaborators through INDAM-GNSAGA funding. Dr. Utano has been actively involved in organizing numerous conferences and workshops on Commutative Algebra and Algebraic Geometry, including the International School on Computational Commutative Algebra and Algebraic Geometry held in Messina in multiple years. She has also participated extensively in outreach activities, organizing mathematics laboratories and teacher training courses focused on innovative teaching methodologies.

• Algebraic Geometry
• Number Theory
• Arithmetic Geometry
• +7 more

Joe Kramer-Miller is an Assistant Professor in the Department of Mathematics at Lehigh University. His contact details include the phone number 610.758.4376 and email jjk221@lehigh.edu, located in room 0017 of Chandler-Ullmann Hall. His research focuses on Algebra and Number Theory, with particular emphasis on arithmetic geometry, p-adic analysis, and Iwasawa theory. Current research interests include the study of Newton polygons on algebraic curves, Frobenius-torsion class group schemes, and the transcendence properties of exponential functions in modular arithmetic contexts. Key research directions involve exploring zeros of zeta functions, monodromy of F-isocrystals, and p-adic estimates of L-functions and exponential sums. His work often intersects with geometric aspects of arithmetic, such as Torelli loci and Newton strata in moduli spaces. Recent articles highlight advancements in understanding local-to-global principles for Newton polygons and logarithmic decay properties of isocrystals. No scientific awards or grants are explicitly listed in the provided information. He has not yet supervised any documented PhD or Master’s students, though this may reflect early career status rather than absence of advising activity. Laboratory or collaborative team affiliations are not detailed in the text. Office location and contact information are provided for direct academic engagement.

• Number Theory
• Arithmetic Geometry
• Elliptic Curves
• +3 more

Matteo Longo is a Full Professor at the University of Padua, affiliated with the Tullio Levi-Civita Department of Mathematics. He leads the Algebraic Geometry and Number Theory research group, focusing on advanced topics in arithmetic geometry. His research bridges elliptic curves, modular forms, and p-adic analysis, with particular emphasis on: p-adic L-functions and their applications Arithmetic of elliptic curves over number fields Iwasawa theory and Selmer groups Heegner points and Darmon points constructions His publication record demonstrates consistent contributions to number theory, with recent works exploring p-adic Maass-Shimura operators, Bloch-Kato Selmer groups, and anticyclotomic Iwasawa theory. The research spans both theoretical frameworks and computational aspects of modern arithmetic geometry. Professor Longo teaches core mathematics courses including Geometry, Number Theory, Topology, and Linear Algebra. Office hours are held Tuesdays at 12:00 in Room 533 of the Department of Mathematics building.

Christopher FreiView profile

Associate Professor

• Arithmetic Geometry
• Analytic Number Theory
• Algebraic Number Theory
• +9 more

Christopher Frei is an Associate Professor at the Institute of Analysis and Number Theory , Graz University of Technology. His research lies at the intersection of arithmetic geometry and analytic and algebraic number theory. Research Trends : His recent work focuses on the distribution of genus numbers in abelian fields, ℓ-torsion bounds in class groups, and rational points on algebraic varieties. He explores arithmetic progressions in quadratic forms, abelian extensions with norm constraints, and applications of o-minimality to Manin's conjecture. Publications : A prolific contributor to number theory, Frei's 15 most recent articles span topics from prime constellations to divisor sums and rational points on cubic surfaces. His collaborations with researchers like Loughran, Newton, and Sofos highlight interdisciplinary approaches combining algebra, analysis, and geometry. Teaching & Outreach : He holds teaching authorization in mathematics at TU Graz and participates in seminars like the Graz-ISTA Number Theory Days .

David BurnsView profile

Professor

• Number Theory
• Iwasawa Theory
• Algebraic K-theory
• +5 more

Professor David Burns is a Professor of Pure Mathematics at King's College London's Department of Mathematics, part of the Faculty of Natural, Mathematical & Engineering Sciences. His research focuses on Number Theory, with particular emphasis on Iwasawa Theory, Stark's Conjecture, and L-functions. He previously studied and held a Junior Research Fellowship at the University of Cambridge before joining King's. He has held visiting positions at institutions including the Universities of Bordeaux, Paris, and Harvard. His research interests include the Tamagawa Number Conjecture of Bloch and Kato, non-commutative Iwasawa Theory, and epsilon constants. He has been recognized with prestigious awards such as the Berwick Prize (1999), a Leverhulme Fellowship (2005), and the Supervisory Excellence Award from King's (2008 and 2023). He has supervised numerous PhD students, many of whom have contributed to leading journals in the field. Education : Undergraduate and graduate studies at the University of Cambridge. Key Research Areas : Iwasawa Theory (including non-commutative aspects) Stark's Conjecture and refinements Euler, Kolyvagin, and Stark systems Algebraic K-theory and homological algebra His publications span over 60 peer-reviewed articles, including foundational work on the Equivariant Tamagawa Number Conjecture and geometric L-functions. Recent work explores p-adic families of special elements and derivatives of Euler systems. Collaborations include projects with leading researchers globally, contributing to areas like arithmetic geometry and non-abelian Iwasawa theory. Grants & Awards : Berwick Prize (London Mathematical Society, 1999) Leverhulme Fellowship (2005) Supervisory Excellence Awards (2008, 2023) He is part of King's Number Theory Group and actively engages in academic leadership, including organizing conferences and editorial roles. His research bridges algebraic geometry, number theory, and homological algebra, with ongoing projects exploring conjectures in arithmetic geometry and Galois module structures.