MAT290 reading seminar: Integer points in polyhera<title></head> <body bgcolor="#ffffff"> <h1><font color=#505080> UC Davis Math 290 reading seminar -- Integer points in polyhedra </font><br> Spring 2009 </h1> <h2> Basic information </h2> <font size="3"><b>location/time:</b> <br> </font> MSB 3106, M 11:00-1:00pm (May 25 is a holiday, we will move to Wednesday that week.)<p> <font size="3"><b>description:</b> <br> </font> The goal of this course is to study the most recent advances in enumeration of integer points in polyhedra. We will start from basic definitions relating to polyhedra, and then after developing the theories of the algebra of polyhedra and the idea of valuation, we describe algorithms that count the number of integer points in rational polytopes. <p> This reading course will be based on Barvinok's new book "Integer points in polyhedra". Below is the table of contents<p> Chapter 1: Introduction<br> Chapter 2: The algebra of polyhedra<br> Chapter 3: Linear transformations and polyhedra<br> Chapter 4: The structure of polyhedra<br> Chapter 5: Polarity<br> Chapter 6: Tangent cones. Decompositions modulo polyhedra with lines<br> Chapter 7: Open polyhedra<br> Chapter 8: The exponential valuation<br> Chapter 9: Computing volumes<br> Chapter 10: Lattices, bases, and parallelepipeds<br> Chapter 11: The Minkowski Convex Body Theorem<br> Chapter 12: Reduced basis<br> Chapter 13: Exponential sums and generating functions<br> Chapter 14: Totally unimodular polytopes<br> Chapter 15: Decomposing a 2-dimensional cone into unimodular cones via continued fractions<br> Chapter 16: Decomposing a rational cone of an arbitrary dimension into unimodular cones<br> Chapter 17: Efficient counting of integer points in rational polytopes<br> Chapter 18: The polynomial behavior of the number of integer points in polytopes<br> Chapter 19: A valuation on rational cones<br> Chapter 20: A "local" formula for the number of integer points in a polytope<p> Our plan is to have 9 lectures to go through this book: 3 lectures for Chapters 1--7, then single lectures covering Chapters 8--9, Chapters 10--12, Chapters 13--14, Chapters 15--16, Chapters 17--18, and Chapters 19--20. I did not plan a lecture on the week of April 27 since I won't be around, but if we are behind schedule by then, we will add one extra lecture at that week. <p> <font size="3"><b>schedule:</b> <br> 3/30: Fu <br> 4/6: Brandon <br> 4/13: Josh <br> 4/20: Matt <br> 4/27: (no lectures) <br> 5/4: Robert <br> 5/11: Jianqiu <br> 5/18: Jesus <br> 5/27 (Wednesday): Matthias <br> 6/1: Fu <br> </body></html>