Introduction to Discrete Geometry MATH-62091

11:00am-1:00pm MTWR in room 115 MSB.

This is a summer enrichment class so, please, be ready to work very hard and have a lot of fun.

Some Suggested Reading

  1. A. Barvinok, "Combinatorics, geometry and complexity of integer points lecture notes".
  2. A. Barvinok, "A Course in Convexity." (Graduate Studies in Mathematics 2002; 366 pp; hardcover Volume: 54).
  3. R. Gardner "The Brunn-Minkowski Inequality."
  4. J. Matousek "Lectures on Discrete Geometry" (Springer, May 2002).
  5. V.D. Milman and G. Schechtman, "Aysmptotic Theory of Finite Dimensional Normed Spaces".
  6. D. Ryabogin, A. Zvavitch, "Analytic methods in convex geometry."
  7. G. Schechtman, "Lecture Notes on Asymptotic Geometric Analysis".
  8. Terence Tao and Van H. Vu, "Additive Combinatorics" (Cambridge Studies in Advanced Mathematics).
  9. Matthias Beck and Sinai Robins, "Computing the continuous discretely: integer point enumeration in polytopes." Springer 2007, Undergraduate Texts in Mathematics.
Instructor
Office hours:
Office:
Office tel.:
E-mail:
WWW of the course :
 Artem Zvavitch
1:00-1:50 MTWR, but the best is to e-mail me and to make an appointment.
364
(330)-672-33-16
zvavitch@math.kent.edu
http://www.math.kent.edu/~zvavitch/IDG2015.html

Please, note the calendar below is just a plan which may be adjusted during the semester!

Date
Lecture Topic
Sugested Reading
Monday (06/08/15)
 Affine Subspace, Hull, Dependens, Basic convexity. Caratheodory Theorem 2, 4
Tuesday (06/09/15)
 Separation Theorem, Radon's lemma, Helly's theorem 2, 4
Wednesday(06/10/15)
Minkowski Theorem/ F. John Theorem 2, 4 / 5, 6, 7.
Thursday (06/11/15)
 Brunn-Minkowski Inequality 3, 6, 7.
Monday (06/15/15)
 Lattices: definition, examples, subspaces, basis and determinant 1.
Tuesday (06/16/15)
Wednesday(06/17/15)
Thursday (06/18/15)
Monday (06/22/15)
 Volume packing lemma 8
Tuesday (06/23/15)
 Minkowski's second Theorem. 8
Wednesday(06/24/15)
Minkowski's second Theorem and applications. 8
Thursday (06/25/15)
 Discrete John Theorem 8
Monday (06/29/15)
 Discrete John Theorem & Arithmetic Sequences 8
Tuesday (06/30/15)
 Lattice-point enumeratos, Ehrhart Series. 9
Wednesday(07/01/15)
Lattice-Point Enumerators of Cube Pyramid. Cross Polytope. 9
Thursday (07/02/15)
 Pick's Theorem, two-dimensional case, Ehrhart polinomials. 9
Monday (07/06/15)
Tuesday (07/07/15)
Wednesday(07/08/15)
Thursday (07/09/15)

TO ARTEM ZVAVITCH'S HOMEPAGE