Jean Gallier, Professor

Computer and Information Science Department
School of Engineering and Applied Science
University of Pennsylvania

Email: jean@cis.upenn.edu
Telephone: (215) 898-4405
Office: GRW 476
Curriculum Vitae   (pdf)
Ancestor "Billy the Kid" Gallier (from Wyoming) (jpg)
Editor's Duties

- Also a member of:

• Department of Mathematics (secondary appointment)
• Center for Human Modelling and Simulation
• GRASP Laboratory
• Institute for Research in Cognitive Science
• Logic and Computation Group

Gran Paradiso (Italy, 2013) Col Rosset (3023 m)   After the storm   Jean   Jean  
Col Bassac Dere (3082 m)   From the Col Bassac Dere   Jean   Descending from Bassac Dere  

Rio, Copacabana (2011) Jean  
Rio Ipanema   Mia, Ipanema  
Sugarloaf, Rio de Janeiro (2011) jaws   Mia  
IMPA, Rio (2011) Moebius strip   Trimester poster   Office  
Rio 2011 (a)   zip   Rio 2011 (b)   zip  
Mont-Blanc, TMB (2011) Jean   Mont Dolent   Celine   Jean   Anne & Jean   cold group  
Mia   Mont-Blanc  
Iguassu, Brazil (2011) Anne   Falls, Argentinian side   Jean   Jean   Jean   Jean   Jean  
Christmas 2011   Demetrius   Bahari   Sylvie   Sylvie and the guys  
Mom, summer 2011  
November 30, 2007. My grandson, Demetrius, his mother, grandfather (me) and father jpg
The Gallier family (before Mia!) at the Col d'Arsine (Hautes Alpes)
Mia eating ice cream, Summer 99
Mia after Eurodysney, Summer 99
Mia in pink, Fall 97
Philippe, Sylvie, My mother June 1999
Mia and me in China, October 97
Sylvie and me on the equator, December 96
More photos Alpes, August 2004
The "Gallier Brothers"

Anne's Artwork

Research Interests

Selected Writings

After 1993: Geometry and its applications (3D graphics, computer vision, robotics), geometric modeling, geometry of curves and surfaces, algebraic geometry, differential geometry, medical imaging

Selected Writings

Book Series: Mathematical Foundations for Computer Vision, Machine Learning, and Robotics

Research Papers and Books

Most Recent Books and Papers

• Mathematical Foundations and Aspects of Discrete Mathematics (html)
  
• Aspects of Harmonic Analysis and Representation Theory   (html)
  
• Homology, Cohomology, and Sheaf Cohomology for Algebraic Topology,
  Algebraic Geometry, and Differential Geometry   (html)
• Linear Algebra and Optimization with Applications to Machine Learning   (html)
  
• Differential Geometry and Lie Groups   (html)
  
• Proofs, Lambda Calculi, Computability, Undecidability, and Complexity.
  An Introduction   (html)
  
• Algebra, Topology, Differential Calculus, and Optimization Theory
  for Computer Science and Machine Learning (html)
• Solving the Elastic Net and Lasso Regression Problems (pdf)
• Aspects of Convex Geometry
  Polyhedra, Linear Programming,
  Shellings, Voronoi Diagrams,
  Delaunay Triangulations   (html)
  
• Notes on Primality Testing and Public Key Cryptography
  Part 1: Randomized Algorithms
  Miller-Rabin and Solovay-Strassen Tests (04/2025)   (pdf)
  
• Spectral Graph Theory of Unsigned and Signed Graphs
  Applications to Graph Clustering: A Survey   (12/2014)
  Posted to arXiv as paper cs.CV arXiv:1311.2492 (pdf)
  
• Introduction to discrete probability (07/2025)   (pdf)

Published Books

Aspects of Harmonic Analysis on Locally Compact Abelian Groups.
World Scientific. (html)   (World Scientific) (Amazon, html)

Aspects of Representation Theory and Noncommutative Harmonic Analysis.
World Scientific. (html)   (Amazon, html)

Homology, Cohomology, and Sheaf Cohomology for Algebraic Topology,
Algebraic Geometry, and Differential Geometry. World Scientific.
(html)   (World Scientific) (Amazon, html)

Differential Geometry and Lie Groups: A Computational Perspective
Geometry and Computing, Vol 12 (html)   (Springer) (Amazon, html)

Differential Geometry and Lie Groups: A Second Course
Geometry and Computing, Vol 13 (html)   (Springer) (Amazon, html)
AI Generated Review (07/2025)   (pdf)

(html)   (World Scientific) (Amazon, html)

(html)   (World Scientific) (Amazon, html)

(html)   (Amazon, html)

(html)   (Springer, html)   (SpringerLink, html)   (Amazon, html)  

Review in Choice pdf   Review in zbMath html   Review in MAA html

(html)   (Springer, html)   (SpringerLink, html)   (Amazon, html)  

Review in zbMath html   Review in Choice pdf

(html)   (Springer, html)   (SpringerLink, html)   (Amazon, html)

Review in MathSciNet (item 2) MathSciNet   Review in zbMath html

(html) Morgan Kaufmann and Amazon.com

Review in MathSciNet (item 1) MathSciNet

Lambda Calculus, Constructive Logics, Unification

All Books

Hot off the Press!

Other Recent Manuscript(s)

• Isometries of Hermitian Spaces   (pdf)
• A Glimpse at Hilbert Spaces   (pdf)
• Parametric Pseudo-Manifolds.
  With M. Siqueira and Dianna Xu (10/2012),
  Differential Geometry and Applications Vol. 30, 702-736 (2012)   (pdf)
  
• Aspects of Harmonic Analysis and Representation Theory   (html)

Algebraic Geometry and Algebra

Lecture Notes

Lecture Notes (html)

More on Research Interests, Teaching, etc: Click here