Professor Masoud Kamgarpour
Professor

Masoud Kamgarpour

Email: 
Phone: 
+61 7 336 56130

Background

I grew up in Iran and moved to Canada towards the end of high school. I completed my undergraduate studies at the University of Waterloo and my PhD at the University of Chicago under the supervision of Valdimir Drinfeld, a Fields Medal winner. I subsequently held postdoctoral positions at the University of British Columbia in Vancouver and the Max Planck Institute for Mathematics in Bonn, before moving to UQ in 2013.

My research has primarily been in geometry and representation theory. I have specifically been interested in the Langlands Program, sometimes described as a Grand Unified Theory of Mathematics. Initiated by Robert Langlands in the 1960s, the program seeks deep connections between apparently different areas of mathematics, using symmetry and representation theory to reveal common structures underlying them.

More recently, I have begun extending these interests towards artificial intelligence. I am particularly interested in the mathematical structure of neural networks and machine reasoning, and in how ideas from mathematics can contribute to understanding and evaluating increasingly capable AI systems. More broadly, I am interested in the implications of AI for mathematics and scientific discovery, AI safety and reliability, and the wider effects of advanced AI on universities, society and public policy.

Availability

Professor Masoud Kamgarpour is:
Available for supervision
Media expert

Qualifications

  • Bachelor of Mathematics, University of Waterloo
  • Masters (Research) of Science, University of Chicago
  • Doctor of Philosophy, University of Chicago

Research interests

  • Geometry, Representation Theory, Neural Network's Internal Structure and Interpretability

    Please see my research website for details: https://sites.google.com/site/masoudkomi/research

Research impacts

My research develops new mathematical tools for understanding symmetry, geometry and complex systems, principally through representation theory and the Langlands Program. This work contributes to areas spanning number theory, geometry, topology and mathematical physics, with longer-term connections to fields such as quantum computing and information security. A major part of my research impact is also through building mathematical capability: my work has been supported by several Australian Research Council projects, including current research on the geometry of character varieties, and I have supervised PhD and MPhil researchers who have gone on to careers in academia and industry.

Search Professor Masoud Kamgarpour’s works on UQ eSpace

19 works between 2009 and 2025
All (19) Journal Article (19)

1 - 19 of 19 works

2025

Journal Article

Arithmetic geometry of character varieties with regular monodromy

Kamgarpour, Masoud, Nam, Gyeonghyeon and Puskás, Anna (2025). Arithmetic geometry of character varieties with regular monodromy. Representation Theory, 29 (11), 347-378. doi: 10.1090/ert/693

Arithmetic geometry of character varieties with regular monodromy

2023

Journal Article

Hypergeometric sheaves for classical groups via geometric Langlands

Kamgarpour, Masoud, Xu, Daxin and Yi, Lingfei (2023). Hypergeometric sheaves for classical groups via geometric Langlands. Transactions of the American Mathematical Society, 376 (5), 3585-3640. doi: 10.1090/tran/8848

Hypergeometric sheaves for classical groups via geometric Langlands

2023

Journal Article

Airy sheaves for reductive groups

Jakob, Konstantin, Kamgarpour, Masoud and Yi, Lingfei (2023). Airy sheaves for reductive groups. Proceedings of the London Mathematical Society, 126 (1), 390-428. doi: 10.1112/plms.12494

Airy sheaves for reductive groups

2022

Journal Article

Character stacks are PORC count

Bridger, Nick and Kamgarpour, Masoud (2022). Character stacks are PORC count. Journal of the Australian Mathematical Society, 115 (3), 1-22. doi: 10.1017/s1446788722000179

Character stacks are PORC count

2021

Journal Article

Geometric Langlands for hypergeometric sheaves

Kamgarpour, Masoud and Yi, Lingfei (2021). Geometric Langlands for hypergeometric sheaves. Transactions of the American Mathematical Society, 374 (12), 8435-8481. doi: 10.1090/tran/8509

Geometric Langlands for hypergeometric sheaves

2020

Journal Article

Rigid connections on P1 via the Bruhat-Tits building

Kamgarpour, Masoud and Sage, Daniel S. (2020). Rigid connections on P1 via the Bruhat-Tits building. Proceedings of the London Mathematical Society, 122 (3), 359-376. doi: 10.1112/plms.12346

Rigid connections on P1 via the Bruhat-Tits building

2020

Journal Article

Jordan decomposition for formal G-connections

Kamgarpour, Masoud and Weatherhog, Samuel (2020). Jordan decomposition for formal G-connections. Graduate Journal of Mathematics, 5 (2), 111-121.

Jordan decomposition for formal G-connections

2019

Journal Article

Complete integrability of the Parahoric Hitchin System

Baraglia, David, Kamgarpour, Masoud and Varma, Rohith (2019). Complete integrability of the Parahoric Hitchin System. International Mathematics Research Notices, 2019 (21) rnx313, 6499-6528. doi: 10.1093/imrn/rnx313

Complete integrability of the Parahoric Hitchin System

2019

Journal Article

A geometric analogue of a conjecture of Gross and Reeder

Kamgarpour, Masoud and Sage, Daniel S. (2019). A geometric analogue of a conjecture of Gross and Reeder. American Journal of Mathematics, 141 (5), 1457-1476. doi: 10.1353/ajm.2019.0038

A geometric analogue of a conjecture of Gross and Reeder

2018

Journal Article

On the image of the parabolic Hitchin map

Baraglia, David and Kamgarpour, Masoud (2018). On the image of the parabolic Hitchin map. Quarterly Journal of Mathematics, 69 (2), 681-708. doi: 10.1093/qmath/hax055

On the image of the parabolic Hitchin map

2017

Journal Article

On the notion of conductor in the local geometric langlands correspondence

Kamgarpour, Masoud (2017). On the notion of conductor in the local geometric langlands correspondence. Canadian Journal of Mathematics, 69 (1), 107-129. doi: 10.4153/CJM-2016-016-1

On the notion of conductor in the local geometric langlands correspondence

2017

Journal Article

Preservation of depth in the local geometric Langlands correspondence

Chen, Tsao-Hsien and Kamgarpour, Masoud (2017). Preservation of depth in the local geometric Langlands correspondence. Transactions of the American Mathematical Society, 369 (2), 1345-1364. doi: 10.1090/tran/6794

Preservation of depth in the local geometric Langlands correspondence

2016

Journal Article

Compatibility of the Feigin-Frenkel isomorphism and the Harish-Chandra isomorphism for jet algebras

Kamgarpour, Masoud (2016). Compatibility of the Feigin-Frenkel isomorphism and the Harish-Chandra isomorphism for jet algebras. Transactions of the American Mathematical Society, 368 (3), 2019-2038. doi: 10.1090/S0002-9947-2014-06419-2

Compatibility of the Feigin-Frenkel isomorphism and the Harish-Chandra isomorphism for jet algebras

2015

Journal Article

Geometrization of principal series representations of reductive groups

Kamgarpour, Masoud and Schedler, Travis (2015). Geometrization of principal series representations of reductive groups. Annales de l'Institut Fourier, 65 (5), 2273-2330. doi: 10.5802/aif.2988

Geometrization of principal series representations of reductive groups

2013

Journal Article

Geometrization of continuous characters of Z(p)(x)

Cunningham, Clifton and Kamgarpour, Masoud (2013). Geometrization of continuous characters of Z(p)(x). Pacific Journal of Mathematics, 261 (1), 95-99. doi: 10.2140/pjm.2013.261.95

Geometrization of continuous characters of Z(p)(x)

2013

Journal Article

Ramified satake isomorphisms for strongly parabolic characters

Kamgarpour, Masoud and Schedler, Travis (2013). Ramified satake isomorphisms for strongly parabolic characters. Documenta Mathematica, 18 (2013), 1275-1300.

Ramified satake isomorphisms for strongly parabolic characters

2011

Journal Article

Maximal representation dimension of finite p-groups

Cernele, Shane, Kamgarpour, Masoud and Reichstein, Zinovy (2011). Maximal representation dimension of finite p-groups. Journal of Group Theory, 14 (4), 637-647. doi: 10.1515/JGT.2010.071

Maximal representation dimension of finite p-groups

2010

Journal Article

Compatible intertwiners for representations of finite nilpotent groups

Kamgarpour, Masoud and Thomas, Teruji (2010). Compatible intertwiners for representations of finite nilpotent groups. Representation Theory, 15 (12), 407-432. doi: 10.1090/S1088-4165-2011-00395-2

Compatible intertwiners for representations of finite nilpotent groups

2009

Journal Article

Stacky abelianization of an algebraic group

Kamgarpour, Masoud (2009). Stacky abelianization of an algebraic group. Transformation Groups, 14 (4), 825-846. doi: 10.1007/s00031-009-9067-8

Stacky abelianization of an algebraic group

Current funding

  • 2025 - 2028
    Geometry of Character Varieties (an ARC Discovery Project administered by Australian National University)
    The Australian National University
    Open grant
  • 2021 - 2026
    Towards logarithmic representation theory of W-algebras
    ARC Discovery Projects
    Open grant

Past funding

  • 2018 - 2021
    Categorical symmetries in representation theory
    ARC Discovery Projects
    Open grant
  • 2014 - 2018
    Problems in the Langlands Program
    ARC Discovery Early Career Researcher Award
    Open grant

Availability

Professor Masoud Kamgarpour is:
Available for supervision

Looking for a supervisor? Read our advice on how to choose a supervisor.

Available projects

  • Algebraic Geometry of Exact Neural Computation

    This project studies the algebraic variety W(p, H) consisting of all parameter choices for a small neural network that exactly compute addition modulo a prime p. RThe aim would be to understand the geometry of these solution spaces themselves: their dimension, irreducible components, singularities, symmetries, and how the geometry changes as the width H increases. The student would combine computational algebra with representation theory and Fourier analysis on cyclic groups, beginning with small cases and looking for structural patterns that can be proved more generally. The broader motivation is mechanistic interpretability: understanding the geometry of all exact implementations of the same computation may reveal whether a task has essentially one internal mechanism or many qualitatively different ones, and how easily learning can move between them.

    This is an Honours project which can later be expanded to a Master's or PhD project.

Supervision history

Current supervision

Completed supervision

Enquiries

Contact Professor Masoud Kamgarpour directly for media enquiries about:

  • AI
  • AI Safety
  • Artificial Intelligence
  • Mathematics

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