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Algebra Seminar - "Ehrhart Theory: When Hilbert functions meet lattice polytopes", Johannes Hofscheier

From October 30, 2017 15:30 until October 30, 2017 16:30
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Johannes Hofscheier
McMaster University

Title:   Ehrhart Theory: When Hilbert functions meet lattice polytopes

Abstract:   In this talk we will give an introduction to Ehrhart Theory with a view toward Hilbert functions. A lattice polytope is the convex hull of finitely many points in real Euclidean space with integer coordinates. They play an important role in many parts of mathematics, e.g., in algebraic geometry, in optimization theory, in discrete mathematics and in the geometry of numbers. To a lattice polytope one associates a ring whose Hilbert function is the Ehrhart function of the polytope. It is a challenging and fascinating open problem how the geometry of the polytope affects the shape of the Hilbert function. We will give an overview of the major unsolved problems in this field and complete our talk with a recent result yielding such a connection. This is joint work with Lukas Katthän and Benjamin Nill.

 

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McMaster University - Faculty of Science

Mailing Address

Department of Mathematics & Statistics
McMaster University

Hamilton Hall, Room 218
1280 Main Street West
Hamilton, Ontario, Canada
L8S 4K1

Contact Information

Office Hours:
8:30 a.m. - 12:00 p.m.
1:00 p.m. - 4:30 p.m.
Telephone Inquiries:
+1 (905) 525-9140 ext.27034
Undergrad Email Inquiries:
undergrad@math.mcmaster.ca

McMaster University - Faculty of Science

Mailing Address

Department of Mathematics & Statistics
McMaster University

Hamilton Hall, Room 218
1280 Main Street West
Hamilton, Ontario, Canada
L8S 4K1

Contact Information

Office Hours:
8:30 a.m. - 12:00 p.m.
1:00 p.m. - 4:30 p.m.
Telephone Inquiries:
+1 (905) 525-9140 ext.27034
Undergrad Email Inquiries:
undergrad@math.mcmaster.ca