# Webinar

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- | * Tuesday, January 12, 5pm Central European Time (UTC+1): <br> '''Sonja Petrović''' (Illinois Institute of Technology) <br> '''''Random Monomial Ideals''''' <br> Joint work with Jesus A. De Loera, Lily Silverstein, Despina Stasi, Dane Wilburne. <br> Inspired by the study of random graphs and simplicial complexes, and motivated by the need to understand average behavior of ideals, we propose and study probabilistic models of random monomial ideals. We prove theorems about the probability distributions, expectations and thresholds for events involving monomial ideals with given Hilbert function, Krull dimension, first graded Betti numbers, and present several experimentally-backed conjectures about regularity, projective dimension, strong genericity, and Cohen-Macaulayness of random monomial ideals. <br> The models for monomial ideals can be used as a basis for generating other types of algebraic objects, and proving existence of desired properties. The talk will feature a tasting of ongoing work in both of these directions. | + | * Tuesday, January 12, 5pm Central European Time (UTC+1): : [https://www.timeanddate.com/worldclock/converter.html?iso=20210112T160000&p1=64&p2=25&p3=270&p4=3999 Other time zones] <br> '''Sonja Petrović''' (Illinois Institute of Technology) <br> '''''Random Monomial Ideals''''' <br> Joint work with Jesus A. De Loera, Lily Silverstein, Despina Stasi, Dane Wilburne. <br> Inspired by the study of random graphs and simplicial complexes, and motivated by the need to understand average behavior of ideals, we propose and study probabilistic models of random monomial ideals. We prove theorems about the probability distributions, expectations and thresholds for events involving monomial ideals with given Hilbert function, Krull dimension, first graded Betti numbers, and present several experimentally-backed conjectures about regularity, projective dimension, strong genericity, and Cohen-Macaulayness of random monomial ideals. <br> The models for monomial ideals can be used as a basis for generating other types of algebraic objects, and proving existence of desired properties. The talk will feature a tasting of ongoing work in both of these directions. |

## Revision as of 07:41, 13 January 2021

## SAGA - Seminar on Applied Geometry and Algebra

Over the last years there has been an immense growth of nonlinear models across the mathematical sciences and its applications to other disciplines. This is fueled by recent theoretical advances in understanding systems of multivariate polynomial equations and inequalities, development of efficient software solving such systems, and an increased awareness of these tools. SIAM SAGA features talks on algebraic geometry and its links to other mathematical branches -- such as combinatorics, algebraic topology, commutative algebra, convex and discrete geometry, tensors and multilinear algebra, number theory, representation theory, and symbolic and numerical computation --, focusing on a variety of applications -- including robotics, optimization, statistics, machine learning, complexity theory, cryptography, coding theory, computer vision, biology, economics, among many others.

**Mailing List**
To stay up-to-date about upcoming talks and receive Zoom invitations please join our mailing list by sending an email to **siam_saga+join@g-groups.wisc.edu**.

- Afterwards you will receive an email which asks you to confirm your wish for subscription by
*replying to that email*. - Finally, you will receive a confirmation email that you became a member.

If you have questions about the mailing list, then email jRodriguez43@wisc.edu (Jose Rodriguez).

**Upcoming Talks**
All seminars take place on the 2nd Tuesday of every month at 5pm CET (UTC+1).

Fill out the SAGA registration to get a personalized Zoom link for each seminar.

- Tuesday, January 12, 5pm Central European Time (UTC+1): : Other time zones

**Sonja Petrović**(Illinois Institute of Technology)

**Random Monomial Ideals**

Joint work with Jesus A. De Loera, Lily Silverstein, Despina Stasi, Dane Wilburne.

Inspired by the study of random graphs and simplicial complexes, and motivated by the need to understand average behavior of ideals, we propose and study probabilistic models of random monomial ideals. We prove theorems about the probability distributions, expectations and thresholds for events involving monomial ideals with given Hilbert function, Krull dimension, first graded Betti numbers, and present several experimentally-backed conjectures about regularity, projective dimension, strong genericity, and Cohen-Macaulayness of random monomial ideals.

The models for monomial ideals can be used as a basis for generating other types of algebraic objects, and proving existence of desired properties. The talk will feature a tasting of ongoing work in both of these directions.

- Tuesday, February 9, 5pm Central European Time (UTC+1):

**Bernd Sturmfels**(MPI MiS Leipzig, UC Berkeley)

**Linear Spaces of Symmetric Matrices**

Real symmetric matrices appear ubiquitously across the mathematical sciences, and so do linear spaces of such matrices. We discuss recent developments concerning their algebraic geometry, with a view towards applications in statistics and optimization.

**Format**
The seminars are held on Zoom:

- 45 minutes of presentation, incl. questions
- informal discussion

Participants can ask questions in the Q&A. The chair will bring forward these questions during and after the talk, and may ask you to unmute yourself to participate in the discussion. Please note that you will be recorded if you activate your audio or video during the seminar.

Each Zoom meeting is provided by SIAM.
The webinars will be recorded and posted in the **SAGA playlist on SIAM’s YouTube account**.

**Organizers**

- Kathlén Kohn (KTH Stockholm)
- Jose Rodriguez (University of Wisconsin - Madison)
- Joachim Rosenthal (University of Zurich)

**Past Talks**
These seminars already happened. But you can fill out the SAGA registration to get a personalized Zoom link for future seminars.

- Tuesday, November 10, 5pm Central European Time (UTC+1): Time zones

**Rekha R. Thomas**(University of Washington)

**When Two Cameras Meet a Cubic Surface**

The set of images captured by an arrangement of pinhole cameras is usually modeled by the multiview variety. The true set is in fact a semialgebraic subset of this variety, arising from the physical restriction that cameras can only image points in front of them. For a pair of cameras, the minimal problem in this semialgebraic setting is given by 5 point pairs, which even in general position, can fail to have a "chiral" reconstruction. I will describe how the combinatorics and arithmetic information of this minimal case is carried by a cubic surface with 27 real lines.

Joint work with Sameer Agarwal, Andrew Pryhuber and Rainer Sinn.

- Tuesday, December 8, 5pm (Central European Time) (UTC+1): Other time zones

**Camilla Hollanti**(Aalto University)

**Coding theoretic framework for private information retrieval**

Private information retrieval (PIR) addresses the question of how to retrieve data items from a database or cloud without disclosing information about the identity of the data items retrieved. The area has received renewed attention in the context of PIR from coded storage systems. Here, the files are distributed over the servers according to a storage code instead of mere replication of data. Alongside with the basic principles of linear codes and PIR, we will review recent PIR capacity results and retrieval schemes. Then, we will introduce our own general framework allowing one to adjust the scheme according to the desired storage overhead and suspected collections of colluding servers. This is achieved by a carefully designed interplay between the algebraic-geometric storage and retrieval codes, coined as the star product scheme.

The talk is based on a collection of joint works with Salim El Rouayheb (Rutgers), Ragnar Freij-Hollanti (Aalto), Oliver Gnilke (Aalborg), Lukas Holzbaur (TU Munich), David Karpuk (F-Secure), Jie Li (Aalto), and Razan Tajeddine (Helsinki).