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
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| 4:00pm |
Dasha Poliakova, SDU Denmark Video
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Wednesday, January 31, 2024
| 10:00am |
Richard Paul Horja Video
|
| 11:30am |
Vasiliki Petrotou: Computer aided experiments II Video
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| 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
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V. Danilov; The geometry of toric varieties
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R. Stanley; Combinatorics and Commutative Algebra
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M. Reid; Graded rings and birational geometry, in Proc. of Algebraic Geometry Symposium (K. Ohno, ed.), Kinosaki 2000
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W. Bruns and J. Herzog; Cohen-Macaulay Rings
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K. Adiprasito; Combinatorial Lefschetz theorems beyond positivity
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K. Adiprasito, G. Yashfe; The Partition Complex: an invitation to combinatorial commutative algebra
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S. Papadakis, V. Petrotou; The characteristic 2 anisotropicity of simplicial spheres
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K. Adiprasito, S. Papadakis, V. Petrotou; Anisotropy, biased pairings, and the Lefschetz property for pseudomanifolds and cycles
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