5/2/22 Through 5/23/22

         

Number Theory Seminar: Randomness of Sequences

                                                                            
Date May 3, 2022
Time 11:00 am
Location via Zoom (contact Kevin Ford)
Speaker Niclas Technau, Caltech
Contact Kevin Ford
Email ford126@illinois.edu
Sponsor n/a
 

The first part of this talk surveys different notions of randomness of one-dimensional sequences. A focal point will be on what is not known about local statistics which go beyond uniform distribution modulo one. The second part is reporting on joint work with Christopher Lutsko and Athanasios Sourmelidis. By employing Fourier analytic tools, this work provides a better understanding of how random slowly growing monomial sequences are - showing that their correlations are Poissonian.         

         

Graph Theory and Combinatorics Seminar: Rational exponents for generalized extremal problems                                                                

Date May 3, 2022
Time 1:00 pm
Location 345 AH
Speaker Anastasia Halfpap (University of Montana)
Contact Sean English
Sponsor N/A
          
Fix a target graph H and a family F of forbidden graphs. The generalized extremal number ex(n, H, F) is the maximum number of H-copies possible in an n-vertex graph which avoids F. Note that when H is an edge, ex(n, H, F) is the ordinary extremal number ex(n, F). After the systematic study of generalized extremal numbers was initiated by Alon and Shikhelman in 2016, the area has received substantial attention. In addition to explicit computation of ex(n, H, F) for specific choices of H, F, many questions in extremal graph theory (e.g., supersaturation, stability) naturally extend to the generalized setting.
 
In 2015, Bukh and Conlon applied the random algebraic method to show that, for any rational r in the interval [1,2], there is a family such that ex(n, F) = Theta(n^r).  Analogously, for a fixed target graph H and a rational number r within an appropriate interval, we may ask whether it is possible to find a forbidden family for which ex(n, H, F) = Theta(n^r). In this talk, we present results on this question for some specific target graphs H, focusing on the case where H is a triangle, for which we show that all rational exponents in [1,3] are realizable. Joint work with Sean English and Bob Krueger. 

 

                                                                
         

Canary Professorship: Candidate Presentation

                                                                                                 
Date May 3, 2022
Time 4:00 pm - 5:00 pm
Location via Zoom
Speaker Jacob Bedrossian (Maryland)
Contact Jared Bronski
Email bronski@illinois.edu
Sponsor n/a
          

Title: Chaos and turbulence in stochastic fluid mechanics: What is it and how could we study it? 

Abstract: In this survey-style talk I discuss the (old) idea of studying turbulence in stochastically-forced fluid equations. I will discuss  efinitions of chaos, anomalous dissipation, and various other predictions by physicists that can be phrased as mathematically precise conjectures in this context. Then, I will discuss some recent work by my collaborators and I on various aspects, namely (1) a straightforward characterization of anomalous dissipation that implies the classical Kolmogorov 4/5 law for 3d NSE (joint with Michele Coti Zelati, Sam Punshon-Smith, and Franziska Weber); (2) the study of "Lagrangian chaos" and exponential mixing of scalars and how it leads to a proof of anomalous dissipation and of the power spectrum predicted by Batchelor in 1959 for the simpler problem of Batchelor-regime passive scalar turbulence (joint with Alex Blumenthal and Sam Punshon-Smith); (3) the more recent proof of "Eulerian chaos" for Galerkin truncations of the Navier-Stokes equations (joint with Alex Blumenthal and Sam Punshon-Smith). 

For other details, please see email sent on behalf of Jared Bronski dated April 27 (sent by P. Currid)

         

Graduate Commutative Algebra & Algebraic Geometry Seminar: Condensation and the Algebraic  Geometry of Topological Algebras

                                                                                                                                                                                                                                                           
Date May 3, 2022
Time 4:00 pm
Location 241 Altgeld Hall
Speaker Brian Shin
Contact Likun Xie
Email likunx2@illinois.edu
Sponsor n/a
          A key foundational input to the success of modern algebraic geometry is the niceness of the category of abelian groups. In particular, it is Grothendieck Abelian with a very nice tensor product. Seeing as many of our favorite algebras come with interesting topologies (e.g. the fields of real and p-adic numbers), one might hope these nice properties persist upon passing to topological abelian groups. Unfortunately, what is typically one's first guess at a definition fails dramatically: the category of topological abelian groups is *terrible*, and there are now many tensor products, each having its own set of pros and cons. These failures make the category of topological abelian groups unsuitable for a foundation of topologo-algebraic geometry. How are we to study algebraic geometry while incorporating the topologies on our rings? In this expository talk, we'll give a brief introduction to Clausen--Scholze's answer to this question: condensed mathematics and analytic geometry.                                                                
         

Department Colloquium: On sphere packings and the hard sphere model

                                                                                                                                                                                      
Date May 4, 2022
Time 4:00 pm
Location 245 Altgeld
Speaker Will Perkins, UIC
Contact Jozsef Balogh
Email jobal@illinois.edu
Sponsor n/a
          The classic sphere packing problem is to determine the densest possible packing of non-overlapping congruent spheres in Euclidean space.  The problem is trivial in dimension 1, straightforward in dimension 2, but a major challenge or mystery in higher dimensions, with the only other solved cases being dimensions 3, 8, and 24.  The hard sphere model is a classic model of a gas from statistical physics, with particles interacting via a hard-core pair potential.  It is believed that this model exhibits a crystallization phase transition in dimension 3, giving a purely geometric explanation for freezing phenomena in nature, but this remains an open mathematical problem. The sphere packing problem and the hard sphere model are closely linked through the following rough rephrasing of the phase transition question: do typical sphere packings at densities just below the maximum density align with a maximum packing or are they disordered? 

I will present results on high-dimensional sphere packings and spherical codes and new bounds for the absence of phase transition at low densities in the hard sphere model.  The techniques used take the perspective of algorithms and optimization and can be applied to problems in extremal and enumerative combinatorics as well.

Lunch is 11:50am at Mandarin Woks, if you  wish to attend, let Jozsef Balogh know before 11am, Dinner plans to be discussed after the lecture.

 

                                                                
         

IRisk Lab Spring 2022 Final Presentations

 
Date May 5, 2022
Time 9:00 am - 2:00 pm
Location 1090 Lincoln Hall
Contact Zhiyu (Frank) Quan
Email ASRM-advising@illinois.edu
Sponsor Illinois Risk Lab
          

You are invited to attend the IRisk Lab's final presentations event during Reading Day, May 5. The event will be held in 1090 Lincoln Hall.

The IRisk Lab is an industry-academic collaboration hub that facilitates integration of discovery-based learning experiences for students, and showcases state-of-the-art research in all areas of risk analysis and advanced analytics.

Whether your are presenting or just want to learn more about the IRisk Lab, come celebrate this semester's research projects.

Event Agenda

  • 9:00 - 9:30 Luyan Sales Data Analysis Project
  • 9:30 - 10:00 Smart Contract of Distributed Insurance Project
  • 10:00 - 10:30 AXIS Systemic Cyber Threats Project
  • 10:30 - 11:00 Automated Machine Learning (AutoML) Project
  • 11:00 - 11:30 Insurtech COUNTRY Financial Loss Model Project
  • 11:30 - 12:00 Insurtech Innovation via Natural Language Processing (NLP) Project
  • 12:00 - 12:30 Building an NLP-Powered Repository and Search Tool for Cyber Risk Literature Project
  • 12:30 - 14:00 Lunch & Networking: pizza and soft drinks will be provided. 

The organizers highly recommend that you take a COVID test and know the result before joining this event.

If you have any questions about the event, please get in touch with professor Zhiyu (Frank) Quan.

 

                                                                 
         

IGL Open House   

Date May 5, 2022
Time 1:00 pm - 4:00 pm
Location Illini Union 314B
Contact Madie Farris
Email mfarris3@illinois.edu
Sponsor IGL
          Join the IGL at our fall open house and poster session and see what everyone in the IGL has been working on this year! All are welcome to stop by anytime 1-4 PM.
                            
         

Conversation Series: Felix Leditzky

Date May 5, 2022
Time 1:00 pm
Location 245 AH
Speaker Felix Leditzky
Contact Vesna Stojanoska
Email vesna@illinois.edu
Sponsor N/A
          One more in the series of informal interviews with faculty in the math department, discussing things like one's career path, challenges, professional inspiration, advice for mathematicians at various career stages, etc.

All are welcome!

(Email Vesna for zoom link.) 

         

Algebra, Geometry & Combinatorics: A Murnaghan-Nakayama rule for Grothendieck polynomials of Grassmannian type

Date May 5, 2022
Time 3:00 pm
Location 347 Altgeld Hall
Speaker Khanh Nguyen Duc
Contact Gidon Orelowitz
Email gidono2@illinois.edu
Phone 917-371-1855
Sponsor N/A
          

The Grothendieck polynomials appearing in the K-theory of Grassmannians are analogs of Schur polynomials. We establish a version of the Murnaghan-Nakayama rule for Grothendieck polynomials of the Grassmannian type. This rule allows us to express the product of a Grothendieck polynomial with a power sum symmetric polynomial into a linear combination of other Grothendieck polynomials.

     
         

Spring 2022 Faculty meeting                                

Date May 5, 2022
Time 4:00 pm
Contact Rebecca Bishop
Email rjbishop@illinois.edu
Phone 217-254-4244
Sponsor Vera Hur
          

The Spring regular meeting of the Department. Please pre-register with Becky Bishop to receive zoom link.

rjbishop@illinois.edu

         

Graduate Student Homotopy Theory Seminar: Calculus for Algebraic Topologists

                                                                                                                                                                  
Date May 6, 2022
Time 3:00 pm
Location 341 Altgeld Hall
Speaker Johnson Tan
Contact Doron Grossman-Naples
Email doronlg2@illinois.edu
Sponsor n/a
   Early on in our mathematical studies, we learn that instead of studying a problem directly it is useful to study a linearization of the problem. For example, to understand a smooth map between manifolds we can look at the resulting linear map between the tangent spaces at a point. In this talk we will be looking at a categorification of this idea through the lens of Goodwillie Calculus. In particular, given a map between sufficiently nice infinity categories we will define what it means for such a map to be "linear" and furthermore how one can approximate by such maps. Time permitting, we will explore further generalizations of this idea.
         

AWM Ice Cream Social

Date May 7, 2022
Time 3:00 pm - 6:00 pm
Location Main Quad (Alternate location in case of inclement weather: 245 AH)
Registration Registration
Contact Yansy Perez
Email yansyp2@illinois.edu
Sponsor Association of Women in Math
 The Association of Women in Mathematics (AWM) will be hosting an Ice Cream Social on Saturday, May 7th, 2022, from 3-6 pm on the Main Quad! In case of rain, we will be in 245 AH.There will be ice cream, (non-alcoholic) drinks, and games! Feel free to also bring your own snacks/dessert to share.

Take this time to hang out with others in our department, celebrate the end of the school year, and congratulate our graduating class! You may also bring your family or a guest!

         

Symplectic and Poisson geometry seminar: Toric Hamiltonian actions in a Poisson context                                                                                                                                

Date May 9, 2022
Time 3:00 pm
Location 347 Altgeld Hall
Speaker Maarten Mol
Contact Joey Palmer
Email jpalmer5@illinois.edu
Sponsor n/a
        This talk concerns toric Hamiltonian actions with momentum maps taking values in regular Poisson manifolds of compact type, or more precisely: toric Hamiltonian actions of regular and proper symplectic groupoids. Examples of these include symplectic toric manifolds, proper Lagrangian fibrations and proper isotropic realizations of Poisson manifolds of compact type. The aim will be to explain the classification of such toric actions in terms of "Delzant polytopes" in the leaf space of the symplectic groupoid. 
         

Graduate Commutative Algebra and Algebraic Geometry Seminar: Introduction to Geometric Invariant Theory II 

Date May 10, 2022
Time 4:00 pm
Location 241 Altgeld Hall
Speaker Zijing Ye
Contact Likun Xie
Email likunx2@illinois.edu
Sponsor n/a

This talk is the second of a series of talks on this topic. In the first talk, I introduced the quotient scheme and linearization of invertible sheaves. In the second talk, I will use them to introduce the stability of points under a group action. Then I will show how the 1-parameter subgroups determine the properties of our group action and stableness. Cookies will be provided as usual.

         

Algebraic Geometry Seminar: Virasoro constraints for moduli of sheaves

Date May 16, 2022
Time 2:00 pm
Location 243 Altgeld Hall
Speaker Rahul Pandharipande, ETH Zurich
Contact Sheldon Katz
Email katzs@illinois.edu
Sponsor n/a

Descendent classes on moduli spaces of sheaves are defined via the Chern characters of the universal sheaf.  I will present several conjectures and results concerning Virasoro constraints for integrals of the descendent classes.

         

Combinatorics Colloquium: The upper tail for triangles in random graphs

Date May 18, 2022
Time 11:00 am
Location Altgeld Hall (room # TBD)
Speaker Wojciech Samotij, Tel Aviv University
Contact Jozsef Balogh
Email jobal@illinois.edu
Sponsor n/a

Abstract: Let $X$ denote the number of triangles in the random graph $G_{n,p}$.  The problem of determining the asymptotics of the logarithimic upper tail probability of $X$, that is, $\log \Pr(X > (1+\delta)\mathbb{E}[X])$, for every fixed positive $\delta$ has attracted considerable attention of both the combinatorics and the probability communities.  We shall present an elementary solution to this problem, obtained recently in a joint work with Matan Harel and Frank Mousset.  The crux of our approach is a simple probabilistic argument, inspired by the work of Janson, Oleszkiewicz and Ruci\’nski, that reduces the estimation of this upper tail probability to a counting problem.

         

Elliptic Cohomology and Conformal Field Theory  

Date May 19, 2022
Time 2:00 pm
Location 343 Altgeld Hall
Speaker Doron Grossman-Naples
Contact Doron Grossman-Naples
Email doronlg2@illinois.edu
Sponsor n/a