Workshop on Combinatorial Geometry

Dates: January 29-31, 2024
Location: 1280 Stanford Dr, Coral Gables, FL 33146 - Lakeside Village Auditorium
Live Video Available via  Zoom

To register, please click here.

Organizer: K. Adiprasito


Schedule

Monday, January 29, 2024

11:00am

Vasiliki Petrotou: Simplicial complexes and face rings of them

We introduce the basic notions of simplicial complexes and their face rings (also known as Stanley-Reisner rings). We discuss about stars and links of a simplicial complex with respect to a face and also to what they correspond on the level of face rings.  Video

12:00pm

Lunch

1:30pm

Karim Adiprasito: Basics in commutative algebra

We discuss some basic commutative algebraic properties of face rings and the Ishida complex. (partly joint with G. Yashfe).  Video

3:00pm

Stavros Papadakis: Duality

We discuss the relation to duality properties, the Gorenstein property, and introduce the notions of the generic Artinian reduction and of the generic anisotropy.  Video

4:30pm

Vasiliki Petrotou: Computer aided experiments I

We discuss how computer aided experimentation led to many key insights, and discuss some of the obtained examples.  Video


Tuesday, January 30, 2024

10:00am

Paul Bressel, University of Los Andes  Video

11:00am

Stavros Papadakis: Combinatorial conjectures, algebraic tools

We give an overview of some combinatorial conjectures, such as the Grünbaum and g-conjectures, and how they relate to deeper algebraic properties.  Video

12:00pm

Lunch

1:30pm

Karim Adiprasito: Anisotropy, biased pairings and the Lefschetz property

We prove generic anisotropy of face rings of simplicial spheres and cycles, the biased pairing property and Hall-Laman relations, and discuss how they relate to the Lefschetz property.  Video

3:00pm

Vasiliki Petrotou: Liaison theory and Kustin-Miller unprojection

We give an introduction to Liaison theory and Kustin-Miller unprojection.  Video

4:00pm

Dasha Poliakova, SDU Denmark  Video


Wednesday, January 31, 2024

10:00am

Richard Paul Horja  Video

11:30am

Vasiliki Petrotou: Computer aided experiments II  Video

12:00pm

Lunch

2:00pm

Stavros Papadakis: Volume polynomial and normalization

We use unprojection theory to give an interpretation of the fundamental class beyond inspirations from geometry.  Video

3:00pm

Semin Yoo, Korean Institute for Advanced Studies

4:00pm

Andrew Sack, UCLA  Video

5:00pm

Karim Adiprasito: Colloquium: Outlook

We discuss further open questions, directions and other applications of our methods.  Video


References

V. Danilov; The geometry of toric varieties

R. Stanley; Combinatorics and Commutative Algebra

M. Reid; Graded rings and birational geometry, in Proc. of Algebraic Geometry Symposium (K. Ohno, ed.), Kinosaki 2000

W. Bruns and J. Herzog; Cohen-Macaulay Rings

K. Adiprasito; Combinatorial Lefschetz theorems beyond positivity

K. Adiprasito, G. Yashfe; The Partition Complex: an invitation to combinatorial commutative algebra

S. Papadakis, V. Petrotou; The characteristic 2 anisotropicity of simplicial spheres

K. Adiprasito, S. Papadakis, V. Petrotou; Anisotropy, biased pairings, and the Lefschetz property for pseudomanifolds and cycles

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