Generated with sparks and insights from 15 sources

Introduction

The field of symmetry research encompasses a vast and interconnected landscape of mathematical, computational, and theoretical investigations. From the fundamental principles governing group theory and algebraic structures to the cutting-edge applications in quantum physics and machine learning, symmetry serves as a unifying concept that bridges multiple disciplines. This comprehensive directory identifies leading researchers and institutions whose work centers on symmetry, symmetrization, and related mathematical structures, providing essential contact information for those seeking to engage with this vibrant research community.

The concept of "symmetrizing" extends beyond mere mathematical abstraction to encompass computational methods, algorithmic approaches, and practical applications across numerous fields. As noted by the Centre for the Mathematics of Symmetry and Computation1, "Our research groups are dedicated to the study of mathematical structures with a high degree of symmetry," covering areas from matrix groups and computational group theory to permutation groups and finite geometry.

1. Leading Research Centers and Institutions

Centre for the Mathematics of Symmetry and Computation (UWA)

The Centre for the Mathematics of Symmetry and Computation1 at the University of Western Australia stands as one of the world's premier institutions dedicated to symmetry research. The center's comprehensive approach encompasses multiple research areas, including:

• Matrix Groups and Computational Group Theory: Developing sophisticated algorithms for studying symmetry using computers
• Permutation Groups: Investigating fundamental properties and their applications to highly symmetric mathematical objects
• Graph Theory (Symmetry and Structure): Addressing important open problems on Cayley graphs
• Finite Geometry and Buildings: Connecting geometry with experimental design, information security, and coding theory
• Matroid Theory: Providing high-level descriptions of minor-closed classes of graphs and binary matroids

The center operates under the broader Mathematics of Symmetry and Computation Research Cluster2, which has received $2.8 million+ in ARC research funding since 2013 and achieved a five (well above world standard) for Pure Mathematics in the 2018 Excellence in Research for Australia outcomes.

For prospective PhD students, the center offers travel funding for Australian candidates to visit Perth and explore research opportunities. Contact: michael.giudici@uwa.edu.au for applications and inquiries.

Boston Symmetry Group

The Boston Symmetry Group3 represents a collaborative network of researchers focusing on the intersection of symmetries and machine learning. The group organizes events for Boston-area researchers interested in topics including:

• Invariant/equivariant neural networks
• Symmetries in learning algorithms
• Graph neural networks
• Applications in physical systems, molecules, and social networks

The group maintains an active mailing list4 for announcements and discussions. Contact: bostonsymmetrygroup@gmail.com for inquiries and participation.

Structure and Symmetry Research at Heriot-Watt University

Heriot-Watt University's Structure and Symmetry research5 encompasses two broad groups: mathematical physics (MP) and algebra, geometry, and topology (AGT). The research focuses on understanding physical phenomena through symmetry analysis and developing theoretical frameworks for complex systems.

The group leads the only UKRI EPSRC Centre for Doctoral Training (CDT) in algebra, geometry, topology, and mathematical physics, jointly administered with the University of Edinburgh and Glasgow University.

2. Individual Researchers by Specialization

Computational Group Theory and Algebraic Symmetry

Michael Giudici - University of Western Australia

Professor Michael Giudici serves as Head of the Department of Mathematics and Statistics at UWA and leads the Centre for the Mathematics of Symmetry and Computation. His research interests encompass group theory and combinatorics, with particular focus on mathematical structures exhibiting high degrees of symmetry.

Contact Information:

• Email: michael.giudici@uwa.edu.au
• Phone: +61 8 6488 3351
• Address: Centre for the Mathematics of Symmetry and Computation, University of Western Australia (M019), 35 Stirling Highway, Perth 6009, Australia

Giudici's work has significantly advanced the field of permutation groups and their applications to symmetric mathematical objects. His research group welcomes PhD applications and offers international research internship opportunities.

Heiko Dietrich - Monash University

Professor Heiko Dietrich at Monash University specializes in computational algebra, particularly group theory and Lie theory. As Associate Dean Graduate Education in the Faculty of Science, he oversees graduate programs while maintaining active research in algorithmic methods of algebra.

Contact Information:

• Email: heiko.dietrich@monash.edu
• Website: users.monash.edu.au/~heikod/6
• Address: School of Mathematics, Monash University, Melbourne, Australia

Dietrich serves as editorial board member for multiple journals including the Journal of Applicable Algebra in Engineering, Communication and Computing, and the Journal of Computational Algebra. His research focuses on developing computational methods for studying group structures and their applications.

Delaram Kahrobaei - CUNY and Multiple Affiliations

Professor Delaram Kahrobaei holds multiple prestigious positions across leading institutions, focusing on the intersection of group theory, cryptography, and quantum computation. Her research addresses critical challenges in post-quantum cryptography through group-theoretic approaches.

Contact Information:

• Primary Email: delaram.kahrobaei61@gc.cuny.edu
• Additional Emails: delaram.kahrobaei@york.ac.uk, delaram.kahrobaei@qc.cuny.edu, dk2572@nyu.edu, kahrobaei@ihes.fr
• Affiliations: Queens College CUNY (Professor), University of York (Honorary Chair of Cybersecurity), NYU Tandon (Adjunct Professor)

Kahrobaei's research interests include post-quantum cryptography, artificial intelligence, applied algebra, and quantum computation. Her work bridges theoretical group theory with practical applications in cybersecurity and quantum algorithms.

Homological Mirror Symmetry and Algebraic Geometry

Tony Pantev - University of Pennsylvania

Professor Tony Pantev specializes in homological mirror symmetry and related areas in algebraic geometry. His research contributes to the Simons Collaboration on Homological Mirror Symmetry, addressing fundamental questions in the intersection of geometry and physics.

Contact Information:

• Email: tpantev@math.upenn.edu
• Phone: (215) 898-5970
• Fax: (215) 573-4063
• Office: 3E4 David Rittenhouse Laboratory
• Office Hours: Monday 4-5pm, Wednesday 4-5pm and by appointment

Pantev's research encompasses Hodge theory, deformation quantization, geometric Langlands theory, and quantum field theory applications. His work bridges classical algebraic geometry with modern theoretical physics through mirror symmetry principles.

Ludmil Katzarkov - University of Miami

Professor Ludmil Katzarkov serves as Executive Director of the Institute of Mathematical Sciences of the Americas and heads the International Laboratory for Mirror Symmetry and Automorphic Forms7. His research focuses on algebraic geometry, symplectic geometry, and the mathematics of string theory.

Contact Information:

• Email: l.katzarkov@miami.edu
• Phone: (305) 284-2279
• Address: Department of Mathematics & Computer Science, University of Miami

Katzarkov's work creates "a new global research platform that combines the study of mirror symmetry with automorphic forms," representing a major advancement in understanding the relationship between geometry and number theory.

Combinatorics and Finite Geometry

John Bamberg - University of Western Australia

Associate Professor John Bamberg specializes in finite incidence geometry, group theory, and algebraic graph theory. His research applies finite geometry to extremal combinatorics and Ramsey theory.

Contact Information:

• Email: john.bamberg@uwa.edu.au
• Website: johnbamberg.github.io8
• Address: Centre for the Mathematics of Symmetry and Computation, Department of Mathematics and Statistics, University of Western Australia

Bamberg serves as handling editor for Combinatorial Theory and Advances in Geometry, with editorial board positions on the Electronic Journal of Combinatorics and Journal of Combinatorial Designs. His research focuses on finite permutation groups and their applications to geometric structures.

Alice Miller - University of Glasgow

Professor Alice Miller specializes in formal verification, model checking, and symmetry reduction techniques. Her research addresses computational challenges in complex software systems through group-theoretic methods.

Contact Information:

• Email: Alice.Miller@glasgow.ac.uk
• Phone: 0141 330 4454
• Address: Room S133, Computing Science, 13 Lilybank Gardens, Glasgow G12 8QQ

Miller's research interests include modelling and verification, abstraction and symmetry reduction, combinatorics, group theory, and graph theory. Her work develops practical applications of symmetry principles in computer science and software engineering.

Topology and Homotopy Theory

J.D. Quigley - University of Virginia

Assistant Professor J.D. Quigley focuses on algebraic topology and homotopy theory applications to geometry, topology, and algebra. He recently received a prestigious NSF CAREER grant totaling just under $500,000 to support his research on symmetry in high-dimensional geometry.

Contact Information:

• Email: mbp6pj@virginia.edu
• Website: quigleyjd.github.io9
• Address: Department of Mathematics, University of Virginia

Quigley co-organizes the Electronic Computational Homotopy Theory online research community and the UVA Topology Seminar. His NSF CAREER project focuses on "Symmetry in geometry, topology, and algebra," representing cutting-edge research in high-dimensional mathematical structures.

3. Editorial and Publication Opportunities

MDPI Symmetry Journal

The MDPI Symmetry Journal10 provides a premier publication venue for symmetry research across multiple disciplines. The journal maintains an active editorial office with dedicated support for authors and reviewers.

Contact Information:

• General Inquiries: symmetry@mdpi.com
• Managing Editor: Ms. Ida Li
• Journal Relations: jr-symmetry@mdpi.com (Ms. Isabella Toth, Ms. Ioana Paunescu)
• Publishing Manager: Dr. Jisuk Kang (jisuk.kang@mdpi.com)
• Address: MDPI, Grosspeteranlage 5, 4052 Basel, Switzerland
• Phone: +41 61 683 77 34

The journal welcomes submissions on symmetry applications in mathematical modeling, computational methods, and theoretical investigations. Special issues regularly address emerging topics in symmetry research.

4. Notable Recognition and Awards

Masaki Kashiwara - 2025 Abel Prize Winner

The 2025 Abel Prize11 was awarded to Masaki Kashiwara "for his fundamental contributions to algebraic analysis and representation theory." Kashiwara's work has reshaped the theory of symmetry through his development of algebraic analysis, bridging differential equations and algebraic geometry.

While specific contact information for Kashiwara wasn't found in the research, his recognition highlights the continued importance of symmetry research in mathematics and its applications to theoretical physics.

5. Research Funding and Opportunities

Simons Foundation Initiatives

The Simons Foundation12 recently announced a call for proposals supporting "inquiry and exploration that expands how both artists and scientists think and conduct research" in symmetry-related fields. This program represents significant funding opportunities for interdisciplinary symmetry research.

Academic Career Opportunities

Several institutions offer postdoctoral positions and PhD opportunities in symmetry research:

• UWA Centre for Symmetry and Computation: Offers 18-month postdoc positions and PhD funding
• Monash University: Provides graduate education opportunities under Dietrich's supervision
• Boston Symmetry Group: Connects researchers with industry and academic opportunities

6. Computational Resources and Software

GAP (Groups, Algorithms, Programming)

The research community actively develops and maintains computational tools for symmetry research. The CoReLG package13 for GAP, developed by researchers including Heiko Dietrich, provides essential computational capabilities for Lie algebra research.

Specialized Software Development

Several researchers maintain active software projects14 supporting symmetry research, including tools for:

• Finite geometry calculations
• Group theory computations
• Algebraic graph theory applications
• Combinatorial optimization

7. International Collaborations and Networks

Institute for Advanced Study Programs

The Institute for Advanced Study15 regularly hosts programs on homological mirror symmetry and related topics, facilitating international collaboration among leading researchers. Contact: math@math.ias.edu for program information.

Global Research Initiatives

The International Laboratory for Mirror Symmetry and Automorphic Forms7 creates "a new global research platform" connecting researchers worldwide in symmetry-related investigations.

Conclusion

The field of symmetry research encompasses a diverse and interconnected community of mathematicians, computer scientists, and theoretical physicists working on fundamental questions with broad practical applications. From the computational group theory advances at UWA to the homological mirror symmetry developments at leading universities, researchers are actively pushing the boundaries of our understanding of symmetry principles.

The contact information provided in this directory represents genuine opportunities for collaboration, mentorship, and research partnerships. Whether seeking PhD supervision, postdoctoral positions, or research collaborations, these researchers and institutions offer pathways for engaging with cutting-edge symmetry research.

For those interested in "symmetrizing" their research or exploring new applications of symmetry principles, the researchers and groups identified here provide excellent starting points for meaningful scientific collaboration. The field continues to evolve rapidly, with new funding opportunities, technological advances, and theoretical breakthroughs creating exciting possibilities for future research directions.

The convergence of classical mathematical symmetry with modern computational methods, quantum applications, and machine learning represents a particularly fertile area for future investigation, making now an ideal time to engage with this vibrant research community.

Appendix: Supplementary Video Resources

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<div class="-md-ext-youtube-widget"> { "title": "Intro to Symmetry (Part 1) | What is Symmetry? | Lines of ...", "link": "https://www.youtube.com/watch?v=dAqDwuHOi4g", "channel": { "name": ""}, "published_date": "Jul 14, 2020", "length": "3:38" }</div>