Western Math Calendar

Sunday	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday
28	29	30	1	2 Colloquium 15:30 Piotr Zwiernik (University of Toronto) Entropic covariance models Colloquium Speaker: Piotr Zwiernik (University of Toronto) "Entropic covariance models" Time: 15:30 - 16:30 Room: MC 107 In covariance matrix estimation often the challenge is to find a suitable model and an efficient method of estimation. Two popular approaches are to impose linear restrictions on the covariance matrix or on its inverse but linear restrictions on the matrix logarithm of the covariance matrix have been also considered. In this talk I will present a general framework for linear restrictions on various transformations of the covariance matrix. This includes the three examples mentioned above. The proposed estimation method relies on solving a convex problem and leads to an estimator that is asymptotically equivalent to the maximum likelihood estimator of the covariance matrix under the Gaussian assumption. After developing a general theory, we restrict our attention to the case where the linear constraints require certain off-diagonal entries to be zero. Here the geometric picture closely parallels what we know for the Gaussian graphical models. In the talk I will focus on the underlying geometry of the problem.	3	4
5	6	7	8	9 Colloquium 15:30 Matthew Satriano (Waterloo) Galois closures and small components of the Hilbert schemes of points Colloquium Speaker: Matthew Satriano (Waterloo) "Galois closures and small components of the Hilbert schemes of points" Time: 15:30 - 16:30 Room: MC 108 Bhargava and the speaker introduced a functorial Galois closure operation for finite-rank ring extensions, generalizing constructions of Grothendieck and Katz-Mazur. In this talk, we use Galois closures to construct new components of Hilbert schemes of points, which are fundamental objects in algebraic geometry whose component structure is largely mysterious. We answer a 35 year old open problem posed by Iarrobino by constructing an infinite family of low dimensional components. This talk is based on joint work with Andrew Staal.	10 Ph.D. Presentation 08:00 Oussama Hamza (Western) Special quotients of Absolute Galois Groups with applications in Number Theory and Pythagorean fields. Ph.D. Presentation Speaker: Oussama Hamza (Western) "Special quotients of Absolute Galois Groups with applications in Number Theory and Pythagorean fields." Time: 08:00 - 09:00 Room: Zoom This talk aims to present the results obtained by Oussama Hamza, during his PhD studies, and his collaborators: Christian Maire, Jan Minac and Nguyen Duy TÃ¢n. Their work precisely focuses on realisation of pro-p Galois groups over some fields with specific properties for a fixed prime p: especially filtrations and cohomology. Hamza was particularly interested on Number and Pythagorean fields. This talk will mostly deal with the last results obtained by Hamza and his collaborators on Formally real Pythagorean fields of finite type (RPF). For this purpose, they introduced a class of pro-2 groups, which is called $\Delta$-RAAGs, and studied some of their filtrations. Using previous work of Minac and Spira, Hamza and his collaborators showed that every pro-2 Absolute Galois group of a RPF is $\Delta$-RAAG. Conversely if a group is $\Delta$-RAAG and a pro-2 Absolute Galois group, then the underlying field is necessarily RPF. This gives us a new criterion to detect Absolute Galois groups. Finally, we also show that the pro-2 Absolute Galois group of a RPF satisfy the Kernel unipotent conjecture jointly introduced, by Minac and TÃ¢n, with the Massey vanishing conjecture, which attracted a lot of interest.	11
12	13	14	15	16 Colloquium 15:30 Rui Dong (Leiden Linguistics Center) Linguistics from a topological viewpoint Colloquium Speaker: Rui Dong (Leiden Linguistics Center) "Linguistics from a topological viewpoint" Time: 15:30 - 16:30 Room: MC 108 TBA Please note: This is a Zoom talk!	17	18
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Sunday

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

Colloquium

15:30 Piotr Zwiernik (University of Toronto) Entropic covariance models

Colloquium

Speaker: Piotr Zwiernik (University of Toronto)

"Entropic covariance models"

Time: 15:30 - 16:30

Room: MC 107

In covariance matrix estimation often the challenge is to find a suitable model and an efficient method of estimation. Two popular approaches are to impose linear restrictions on the covariance matrix or on its inverse but linear restrictions on the matrix logarithm of the covariance matrix have been also considered. In this talk I will present a general framework for linear restrictions on various transformations of the covariance matrix. This includes the three examples mentioned above. The proposed estimation method relies on solving a convex problem and leads to an estimator that is asymptotically equivalent to the maximum likelihood estimator of the covariance matrix under the Gaussian assumption. After developing a general theory, we restrict our attention to the case where the linear constraints require certain off-diagonal entries to be zero. Here the geometric picture closely parallels what we know for the Gaussian graphical models. In the talk I will focus on the underlying geometry of the problem.

Colloquium

15:30 Matthew Satriano (Waterloo) Galois closures and small components of the Hilbert schemes of points

Colloquium

Speaker: Matthew Satriano (Waterloo)

"Galois closures and small components of the Hilbert schemes of points"

Time: 15:30 - 16:30

Room: MC 108

Bhargava and the speaker introduced a functorial Galois closure operation for finite-rank ring extensions, generalizing constructions of Grothendieck and Katz-Mazur. In this talk, we use Galois closures to construct new components of Hilbert schemes of points, which are fundamental objects in algebraic geometry whose component structure is largely mysterious. We answer a 35 year old open problem posed by Iarrobino by constructing an infinite family of low dimensional components. This talk is based on joint work with Andrew Staal.

Ph.D. Presentation

08:00 Oussama Hamza (Western) Special quotients of Absolute Galois Groups with applications in Number Theory and Pythagorean fields.

Ph.D. Presentation

Speaker: Oussama Hamza (Western)

"Special quotients of Absolute Galois Groups with applications in Number Theory and Pythagorean fields."

Time: 08:00 - 09:00

Room: Zoom

This talk aims to present the results obtained by Oussama Hamza, during his PhD studies, and his collaborators: Christian Maire, Jan Minac and Nguyen Duy TÃ¢n.

Their work precisely focuses on realisation of pro-p Galois groups over some fields with specific properties for a fixed prime p: especially filtrations and cohomology. Hamza was particularly interested on Number and Pythagorean fields.

This talk will mostly deal with the last results obtained by Hamza and his collaborators on Formally real Pythagorean fields of finite type (RPF). For this purpose, they introduced a class of pro-2 groups, which is called $\Delta$-RAAGs, and studied some of their filtrations. Using previous work of Minac and Spira, Hamza and his collaborators showed that every pro-2 Absolute Galois group of a RPF is $\Delta$-RAAG. Conversely if a group is $\Delta$-RAAG and a pro-2 Absolute Galois group, then the underlying field is necessarily RPF. This gives us a new criterion to detect Absolute Galois groups.

Finally, we also show that the pro-2 Absolute Galois group of a RPF satisfy the Kernel unipotent conjecture jointly introduced, by Minac and TÃ¢n, with the Massey vanishing conjecture, which attracted a lot of interest.

Colloquium

15:30 Rui Dong (Leiden Linguistics Center) Linguistics from a topological viewpoint

Colloquium

Speaker: Rui Dong (Leiden Linguistics Center)

"Linguistics from a topological viewpoint"

Time: 15:30 - 16:30

Room: MC 108

TBA Please note: This is a Zoom talk!

Sunday	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday
			1	2 Colloquium 15:30 Piotr Zwiernik (University of Toronto) Entropic covariance models Colloquium Speaker: Piotr Zwiernik (University of Toronto) "Entropic covariance models" Time: 15:30 - 16:30 Room: MC 107 In covariance matrix estimation often the challenge is to find a suitable model and an efficient method of estimation. Two popular approaches are to impose linear restrictions on the covariance matrix or on its inverse but linear restrictions on the matrix logarithm of the covariance matrix have been also considered. In this talk I will present a general framework for linear restrictions on various transformations of the covariance matrix. This includes the three examples mentioned above. The proposed estimation method relies on solving a convex problem and leads to an estimator that is asymptotically equivalent to the maximum likelihood estimator of the covariance matrix under the Gaussian assumption. After developing a general theory, we restrict our attention to the case where the linear constraints require certain off-diagonal entries to be zero. Here the geometric picture closely parallels what we know for the Gaussian graphical models. In the talk I will focus on the underlying geometry of the problem.	3	4
5	6	7	8	9 Colloquium 15:30 Matthew Satriano (Waterloo) Galois closures and small components of the Hilbert schemes of points Colloquium Speaker: Matthew Satriano (Waterloo) "Galois closures and small components of the Hilbert schemes of points" Time: 15:30 - 16:30 Room: MC 108 Bhargava and the speaker introduced a functorial Galois closure operation for finite-rank ring extensions, generalizing constructions of Grothendieck and Katz-Mazur. In this talk, we use Galois closures to construct new components of Hilbert schemes of points, which are fundamental objects in algebraic geometry whose component structure is largely mysterious. We answer a 35 year old open problem posed by Iarrobino by constructing an infinite family of low dimensional components. This talk is based on joint work with Andrew Staal.	10 Ph.D. Presentation 08:00 Oussama Hamza (Western) Special quotients of Absolute Galois Groups with applications in Number Theory and Pythagorean fields. Ph.D. Presentation Speaker: Oussama Hamza (Western) "Special quotients of Absolute Galois Groups with applications in Number Theory and Pythagorean fields." Time: 08:00 - 09:00 Room: Zoom This talk aims to present the results obtained by Oussama Hamza, during his PhD studies, and his collaborators: Christian Maire, Jan Minac and Nguyen Duy TÃ¢n. Their work precisely focuses on realisation of pro-p Galois groups over some fields with specific properties for a fixed prime p: especially filtrations and cohomology. Hamza was particularly interested on Number and Pythagorean fields. This talk will mostly deal with the last results obtained by Hamza and his collaborators on Formally real Pythagorean fields of finite type (RPF). For this purpose, they introduced a class of pro-2 groups, which is called $\Delta$-RAAGs, and studied some of their filtrations. Using previous work of Minac and Spira, Hamza and his collaborators showed that every pro-2 Absolute Galois group of a RPF is $\Delta$-RAAG. Conversely if a group is $\Delta$-RAAG and a pro-2 Absolute Galois group, then the underlying field is necessarily RPF. This gives us a new criterion to detect Absolute Galois groups. Finally, we also show that the pro-2 Absolute Galois group of a RPF satisfy the Kernel unipotent conjecture jointly introduced, by Minac and TÃ¢n, with the Massey vanishing conjecture, which attracted a lot of interest.	11
12	13	14	15	16 Colloquium 15:30 Rui Dong (Leiden Linguistics Center) Linguistics from a topological viewpoint Colloquium Speaker: Rui Dong (Leiden Linguistics Center) "Linguistics from a topological viewpoint" Time: 15:30 - 16:30 Room: MC 108 TBA Please note: This is a Zoom talk!	17	18
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