Tea in POT 745 at 3:14 pm = π time

Speaker:  Mihai Ciucu, Indiana University

Title:  Cruciform regions and a conjecture of Di Francesco

Abstract:

The problem of finding formulas for the number of tilings of lattice regions goes back to the early 1900's, when MacMahon proved (in an equivalent form) that the number of lozenge tilings of a hexagon is given by an elegant product formula. In 1992, Elkies, Kuperberg, Larsen and Propp proved that the Aztec diamond (a certain natural region on the square lattice) of order n has 2^n(n+1)/2 domino tilings. A large related body of work developed motivated by a multitude of factors, including symmetries, refinements and connections with other combinatorial objects and statistical physics. It was a model from statistical physics that motivated the conjecture which inspired the regions we will discuss in this talk.

In recent work on the twenty vertex model, Di Francesco was led to a conjecture which states that the number of domino tilings of a certain family of regions on the square lattice is given by a product formula reminiscent of the one giving the number of alternating sign matrices. These regions, denoted T_n, are obtained by starting with a square of side-length 2n, cutting it in two along a diagonal by a zigzag path with step length two, and gluing to one of the resulting regions half of an Aztec diamond of order n-1. Inspired by the regions T_n, we construct a family of cruciform regions C_m,n^a,b,c,d generalizing the Aztec diamonds and we prove that their number of domino tilings is given by a simple product formula. Since (as it follows from our results) the number of domino tilings of the region T_n is a divisor of the number of tilings of the cruciform region C_2n-1,2n-1^n-1,n,n,n-2, the special case of our formula corresponding to the latter can be viewed as partial progress towards proving Di Francesco's conjecture.

Dr. Lisa Bhungalia is a political geographer specializing in race, violence, and empire with a regional focus on the Southwest Asian and North African region. Her research explores the relationship between US empire, late modern warfare, and transnational linkages and encounters between the US and North Africa/Middle East region. 

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Borrowing from scholarship in map studies, critical cartography, queer media studies. and critical bibliography, this talk examines the utility of queer geographic information as expressed through its materiality. Through an examination of queer spatial information from the 1930s to the mid-2000s—primarily travel guides and maps but also magazines, postcards, and advertising—this talk explores two main arguments. Firstly, that the physical arrangement of queer spatial media and the work individuals undertook to collect, circulate, protect, and keep up to date this information in the pre-digital era reveals this information's politics and perils. Secondly, the presentation argues that to understand these social currents there is a need for renewed attention to physical media and physical interaction during the archival research process. The talk concludes by examining the presenters’ efforts in developing an archival collection of queer spatial information.

“Seeds help me keep my proximity to all the things I don’t want to forget, through stories, flavors and recipes”

Turkish seed keeper Mehmet Öztan will discuss how seeds connect him to his memories of people, places and time; and how they helped him build relations with people of other cultural backgrounds while he is far away from his homeland and living in rural West Virginia. Öztan will also share his thoughts about racism in seed industry as an immigrant seed professional with a decade of experience in the field.

"Communal data governance: digital access and protection in indigenous territories of Oaxaca, Mexico"

With expanding internet coverage,  the issues of access to information in native languages and data protection have become increasingly important in indigenous communities in Mexico, long subject to discrimination and extractivist economic practices. This talk examines the issue of communal data governance in Oaxaca, exploring how indigenous rights and traditions of self governance are being extended into the realm of Information and Communication Technologies.  

"Necropolitics, Border Walls, and a Murder of Jim/Juan Crow in the Mexico-US Frontera"

Across the Mexico-US borderlands, overlapping white supremacist and Anglo-nationalist movements are building private walls as monuments to Donald Trump. Many social justice activists and ecological stewards have warned that these Trumpist border walls present specific and new threats to social and ecological landscapes, particularly along the riparian sections of the borderlands. To slow their building and, even, topple these walls, many activists and ecological caretakers are working to fortify networks with similar efforts elsewhere. In an effort to provide analyses useful to such justice endeavors, I employ Achille Mbembe’s concept of necropolitics to situate the borderland activist struggles against the Trumpist walls within a broader context of struggle against the commemoration of racist terror in the US South. Specifically, I use Mbembe’s theorization of necropolitical deathworlds to illustrate some potential common cause linking protests against Trumpist walls in the Paso del Norte region of the Mexico-US border with a Black Lives Matter/Say Her Name coalition that is bringing down Confederate monuments in central Texas. In placing these movements in connection with each other, I highlight a synergy of the white supremacy of Jim Crow with the Anglo nationalism behind a Juan Crow variant of racist terror and anti-immigrant hatred driving the Trumpist wall constructions. Recognition of this convergence is one way, I maintain, for identifying opportunities for making common cause across Americas’ myriad struggles to destroy the racist monuments that glorify the necropolitical legacy of racist colonialism and its ongoing social and ecological devastation.

As the term ``big data'' appears more and more frequently in our daily life and research activities, it changes our knowledge of how large the scale of the data can be and challenges the application of numerical analysis for performing statistical calculations on computers. In this talk, I will focus on two basic statistics problems---sampling a multivariate normal distribution and maximum likelihood estimation---and illustrate the scalability issue that many traditional numerical methods are facing. The large-scale challenge motivates us to develop linearly scalable numerical linear algebra techniques in the dense matrix setting, which is a common scenario in data analysis. I will present several recent developments on the computations of matrix functions and on the solution of a linear system of equations, where the matrices therein are large-scale, fully dense, but structured. The driving ideas of these developments are the exploration of the structures and the use of fast matrix-vector multiplications to reduce the quadratic cost in storage and cubic cost in computation for a general dense matrix. ``Big data'' provides a fresh opportunity for numerical analysts to develop algorithms with a central goal of scalability in mind. Scalable algorithms are key for convincing statisticians and practitioners to apply the powerful statistical theories on large-scale data that they currently feel uncomfortable to handle.