First Organizational meeting : Date : Monday, September 20, 2010. Time : 4 PM. Venue : MSB 2112.
Please let me know if the date/time is inconvenient for anyone interested in the RFG !
Activites for Fall 2010 :
UPDATE : The regular meeting time and venue for the Fall research seminar has been decided. We meet on Mondays and Wednesdays, 4:15-5:30 pm in MSB 2240. Please see the associated weblink below for more details.
1. Research seminar covering topics including, but not limited to,
a) application of Geometry of Numbers in Integer Programming, specially the recent work in cutting plane theory.
I plan to concentrate on research topics related to maximal lattice-point free convex sets.
b) more classical techniques in Combinatorial optimization such as polyhedral combinatorics.
Extended Reformulations for combinatorial optimization problems is a topic that I would like to learn in depth in this context.
c) An ambitious attempt at combining generating function techniques with cutting plane theory. Initial talks and lectures would
cover the relevant theory in both fields. We will try to explore if we can somehow derive strong cutting planes using information from generating functions;
as well as the possiblity of updating/simplifying generating functions using information from cutting planes.
Literature : There are a number of excellent surveys and tutorials covering the topics in a) and b) above. My own research experience in
cutting plane theory would be the source for many of the lectures. I will attempt to efficiently bring the participants upto speed with current
research and then think about open research problems. I also plan to cover some of the chapters from the book "A Course in Convexity" by Alexander Barvinok.
Organized lectures by leading researchers in the area will announced as and when details are finalized.
2. Depending on enthusiasm for participation, I would very much like to run a reading course on the interaction of lattices and convex polyhedra.
The goal would be to cover the book "Integer Points in Polyhedra" by Alexander Barvinok and then explore research problems in this
field. Prof. Fu Liu ran a reading course a couple of years ago on this same topic. However, if there are enough people who are interested in
seeing this (because they were not around for Prof Liu's course), I would like to run this concurrently with my regular research seminar. We can
discuss this further on our first meeting for the year.
3. Prof. DeLoera is planning to run a reading seminar on "Recent Advances in Linear Optimization". We might see some exciting new results
like the recent counterexample to the Hirsch Conjecture, strongly polynomial time algorithms for LP, smoothed analysis of algorithms and so on.
Activites for Winter are recorded here.
Activities for Spring :
We are running two parallel activities this Spring.
READING CLUB WITH MATROID RFG
One of the activities will be run jointly with Dr. Andrew Berget's RFG on Matroid Theory. We will be covering some topics from the book Topics in Hyperplane Arrangements, Polytopes and Box Splines by De Concini and Procesi. We meet every Thursday at 3:00pm in MSB 3106. If you are interested in presenting a lecture, please contact Andrew at berget [at] math [dot] ucdavis [dot] edu.
JOURNAL CLUB ON ASPECTS OF LINEAR OPTIMIZATION AND RELATED DISCRETE GEOMETRY
The second activity will be a journal club. We will meet on Wednesdays at 4:40pm in MSB 3106 and will be reading a variety of papers of interest, most of which are recent exciting developments in the field of optimization. We will attempt to provide a list of these papers below, and potentially a schedule of when these papers will be discussed.
The activities for this journal club are recorded here.