Hemanshu Kaul

Department of Applied Mathematics
Illinois Institute of Technology
10 West 32nd Street
Chicago, IL 60616

Tel: (312) 567-3128
Fax: (312) 567-3135
e-mail: kaul at iit.edu
Webpage: http://www.math.iit.edu/~kaul

General Information

I am an associate professor in the Department of Applied Mathematics at Illinois Institute of Technology. Here is my departmental contact page.

I graduated from the Department of Mathematics, University of Illinois at Urbana-Champaign. I was a member of the Combinatorics and Graph Theory research group, and the Simulation and Optimization laboratory (a part of Operations Research at UIUC). My dissertation was co-directed by Professors Sheldon Jacobson and Douglas West.

I was an AMS Project NExT Fellow, 2007-08.

Earlier, I studied at Indian Institute of Technology, Bombay and at St. Stephen's College, Delhi.

My Curriculum Vitae.


A book that I co-edited with H.M. Mulder:
Advances in Interdisciplinary Applied Discrete Mathematics, Interdisciplinary Mathematical Sciences, Volume 11, World Scientific Publishing, 2010, 275pp.
Here is the book's Cover, Title Page, and Introduction.
Available at the Publisher's site, and on Amazon.



| Research Interests | | Research Activities | | Conferences & Seminars | | Teaching | | Miscellaneous |

Research Interests

I work in the fields of Discrete Mathematics and Operations Research.
My research interests lie in Graph Theory, Discrete Optimization, Discrete Geometry, Probabilistic Discrete Structures, and their interdisciplinary applications in Civil Engineering (Transportation Networks), ECE (Renewable Energy distribution), Computer Science (Network Security), Homeland Security, etc.

Discrete optimization models arise naturally in all branches of discrete mathematics and their applications. My motivation is to develop the understanding of hard optimization problems through a variety of approaches - using probabilistic and combinatorial tools to tackle problems, developing and analyzing the complexity of exact and approximation algorithms, developing both practical and theoretical aspects of heuristics, and understanding local search algorithms and multi-objective optimization. I work with collaborators in Computer Science and in Engineering to apply these methodologies to interdisciplinary applications.
My past research has included topics in Stochastic Combinatorial Optimization, Network Optimization, Exact Combinatorial Algorithms, Meta-Heuristics, Local Search Landscapes, Multi-objective Discrete Optimization.

Graph Theory is the language used to describe and study binary relations, which explains its numerous and varied applications in engineering, social sciences, and natural sciences. For nontrivial applications of graph theory, it is essential to understand the substructures (and corresponding properties) in graphs and the parameters that imply their existence. My aims in graph theory are two-fold - to deepen the theoretical understanding of graphs as discrete structures, and to apply graph-theoretic techniques to problems in other disciplines.
My past research has included topics in Graph Packing, Graph Coloring, MAX-CUT or Largest Bipartite Subgraph problem, Maximum Independent (Stable) Set problem, Maximum Planar subgraph problem, Graph Layout problems.

Here is the departmental research page at IIT.

Check out my list of Journals in discrete mathematics and related fields , which also give an indication of my research interests.



Research and Academic Activities

Papers and Publications with summaries and talks.

Conferences, Colloquia, and Seminars


Conferences and Seminars Organized

Conferences

Workshop in honor of Professor Douglas West's 60th Birthday, June 2014, IMA, Minneapolis, (Co-organizer).

Special Session on Graphs and Hypergraphs at AMS Meeting, November 2010, University of Notre Dame, (Co-Organizer).

47th Midwest Graph Theory Conference, November 2008, IIT, Chicago, (Co-Organizer).

Special Session on Graph Theory at AMS Meeting , April 2008, Indiana University, Bloomington, (Co-Organizer).

Project NExT panel discussion on `Early Career Grants: possible sources and proposal writing', January 2008, Joint Mathematics Meeting, San Diego, (Co-Organizer).

Special Session on Graph Theory at AMS Meeting, October 2007, Depaul University, Chicago, (Co-Organizer).

Seminars

IIT Applied Math Colloquium (Organizer 2008-09).

IIT Discrete Applied Math Research Seminar (Organizer 2007-08, 2010-11, 2012-13).

Pan-IIT Interdisciplinary Seminar Series on ``Networks and Optimization'', IIT, Spring 2009 (with R. Ellis and M. Pelsmajer).

Chicago Area Discrete Math Reading Seminar (Co-Organizer 2006-2008).




Current Teaching

Fall 2014
Math 100: Introduction to the Profession
Math 454/553: Graph Theory/ Discrete Applied Math I

Math 591: M.S. Thesis Research.
Math 691: Ph.D. Thesis research.


Curriculum Development

At IIT :

Math 332: Elementary Linear Algebra:Syllabus; Discussion and Course.
Math 410: Number Theory: Syllabus; Discussion and Course.
Math 435: Linear Optimization:Syllabus; Discussion and Course.
Math 486/522: Mathematical Modeling:.
Math 535: Linear Optimization: Syllabus; Discussion and Course.
Math 554: Discrete Applied Math II (Modern Methods in Combinatorics): Syllabus and discussion; Course.

At UIUC :

Topics in Probabilistic Methods for Discrete Mathematics: Proposal and Course.
Discrete and Convex Geometry : Proposal.


Teaching Experience

At IIT :

Spring 2014
Math 486/522: Mathematical Modeling
Math 435/535: Linear Optimization/ Optimization I

Math 591: M.S. Thesis Research.
Math 691: Ph.D. Thesis research.

Fall 2013
On Sabbatical, visiting universities in China and South Korea.
Math 691: Ph.D. Thesis research.
Math 591: M.S. Thesis research.

Summer 2013
Math 554: Reading course on Graph Theory.
Math 691: Ph.D. Thesis research.

Spring 2013
Math 410: Number Theory
Math 554: Discrete Applied Math II (Mathematical Methods in Discrete Math)
Math 691: Ph.D. Thesis research.

Fall 2012
Math 430: Applied Abstract Algebra
Math 454/553: Graph Theory/ Discrete Applied Math I
Math 100: Lectures and problems on 'Visual Combinatorial Proofs', 'Planar Graphs and Graph Drawing', and 'Graph Coloring'.
Math 691: Ph.D. Thesis research.

Spring 2012
Math 251: Multivariable and Vector Calculus
Math 435/535: Linear Optimization/ Optimization I
Math 491: Research with undergrads.
Math 691: Ph.D. Thesis research.

Fall 2011
Math 152: Calculus II.
Math 332: Elementary Linear Algebra (Matrices)
Math 100: Lectures and problems on 'Visual Combinatorial Proofs', 'Planar Graphs and Graph Drawing', and 'Graph Coloring'.
Math 491: Research with undergrads.
Math 691: Ph.D. Thesis research.

Summer 2011
Math 591: M.S. Thesis research.

Spring 2011
Math 251: Multivariable and Vector Calculus.
Math 554: Discrete Applied Math II (Mathematical Methods in Discrete Math)
Math 591: M.S. Thesis research.

Fall 2010
Math 410: Number Theory
Math 454/553: Graph Theory/ Discrete Applied Math I
Math 100: Lectures and problems on 'Visual Combinatorial Proofs', 'Planar Graphs and Graph Drawing', and 'Graph Coloring'.

Summer 2010
Math 491: Research with undergrad on 'Fall coloring of Graphs'.
Math 597: Reading course with grad student on advanced topics in Combinatorial Optimization.

Spring 2010
Math 435/535: Linear Optimization/ Optimization I
Math 453: Combinatorics
Math 491: Research with undergraduate student on 'Fall Coloring in Graphs'.

Fall 2009
Math 332: Elementary Linear Algebra (Matrices)
Math 591: Research with graduate student on 'computational art gallery problem'.
Math 491: Independent reading with undergrad student on advanced topics in 'Extremal Graph Theory'.
Independent reading with undergrad student on introduction to 'Stochastic Optimization'.
Math 100: Lectures and problems on 'Visual Combinatorial Proofs', 'Planar Graphs and Graph Drawing', and 'Graph Coloring'.

Spring 2009
Math 410: Number Theory
Math 554: Discrete Applied Math II (Mathematical Methods in Discrete Math)
Math 591: M.S. Thesis research.
Math 593: Graduate Student Seminar coordinator.

Fall 2008
Math 332: Elementary Linear Algebra (Matrices)
Math 491: Research with undergrad on 'Guarding Orthogonal Art gallery with holes'.
Math 100: Lecture on 'Graph Coloring'; Project (expository report and computer implementation) on 'Theory and Algorithms for Stable Matchings' with 2 students.
Math 593: Graduate Student Seminar coordinator.

Summer 2008
Math 491: Research with undergrads on 'Guarding Orthogonal Art gallery with holes' and on 'Fall coloring of Graphs'.

Spring 2008
Math 435/ 535: Linear Optimization/ Optimization I
Math 491: Research with undergrad on 'Fall coloring of Graphs'.

Fall 2007
Math 251: Multivariable and Vector Calculus
Math 454/ 553: Graph Theory/ Discrete Applied Math I
Math 100: Lectures on 'Logical reasoning'.

Spring 2007
Math 410: Number Theory

Fall 2006
Math 151-006: Calculus I
Math 332-001: Elementary Linear Algebra (Matrices)
Math 100: Lecture on 'Graph Optimization'; Project (expository report and computer implementation) on 'Theory and Algorithms for Stable Matchings' with 3 students.

At UIUC :

Fall 2005 and earlier
Topics in Probabilistic Methods for Discrete Mathematics
Other Courses and Course Proposals




Miscellaneous

Favorite Links: Discrete Math, Operations Research and Applied Probability; General Mathematical Resources; Academic Homepages; Software Resources; General References; Newspapers, Magazines and Blogs; Weather; Books and Music; Culinary Resources; Movies and Entertainment; Puzzles and Humor; Sports; Travel; Search Engines; Urbana-Champaign.

Journals (etc.) in Discrete Mathematics and related fields -- a resource maintained by me.










( My name is often misspelled, so here are some other common spellings : himanshu kaul / himanshu koul / hemanshu koul )