Department of

# Mathematics

Seminar Calendar
for events the day of Wednesday, March 10, 2021.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Wednesday, March 10, 2021

3:00 pm in Zoom,Wednesday, March 10, 2021

#### Preparing Pre-Service Math Educators for Teaching Emerging Bilinguals

###### Tasha Austin (Rutgers)

Abstract: Many teacher educators have redoubled efforts to be as precise and impactful as ever with instruction with the recent challenges of remote instruction and pandemic inequities. Preparing pre-service teachers to instruct emerging bilingual populations remains a critical undertaking as we identify high-leverage considerations that will yield the best results for our multilingual learners in general education settings. Among these considerations are acknowledging the legislative and theoretical precedents to centering the specific strengths and needs of these populations. For math educators in particular, practical considerations include valuing community, inquiry, and representation in the learning environment as well as discipline-specific language demands and scaffolding. In this session I will speak to the specific courses I teach in seven-week iterations which span the theoretical and practical steps for preparing pre-service math educators to teach emerging bilinguals.

Tasha Austin is a doctoral student and lecturer in Language Education at the Rutgers Graduate School of Education and the Teacher Education Special Interest Group Representative for NJTESOL-NJBE. As founder of Premise LLC, she supports schools with innovative and humanizing pedagogies. Her research uses critical race theory and Black feminist epistemologies to qualitatively examine language, identity and power, and the ways in which anti-Blackness emerges in language education and language teacher preparation.

6:00 pm in Zoom | Register at http://bit.ly/MathWithoutBorders,Wednesday, March 10, 2021

#### “Structure-preserving discretization of differential calculus and geometry”

###### Anil Hirani, associate professor (University of Illinois Urbana-Champaign, Department of Mathematics)

Abstract: Two important aspects of the structure of differential calculus are the chain and product rules. On manifolds, chain rule generalizes to the exterior derivative commuting with pullback by smooth maps. The product rule generalizes to a rule for the exterior derivative of wedge product of differential forms. These properties, especially the product rule, may be used as one of the defining properties for a covariant derivative in differential geometry. What if one is developing calculus and geometry for non-smooth spaces. One such application is the development of a discrete exterior calculus and discrete differential geometry for simplicial complexes (e.g. triangle meshes and tetrahedral meshes). What should play the role of the smooth maps, the exterior derivative, the wedge product and the covariant derivative so that we can speak of the above structural properties of calculus and geometry in this discrete setting? I will use examples to describe such a discrete calculus and geometry we have been developing. This will be a survey of some old ideas and some new developments. The newer developments are joint work with Mark Schubel (Apple Inc.) and Daniel Berwick-Evans (UIUC).

6:55 pm in Zoom | Register at http://bit.ly/MathWithoutBorders,Wednesday, March 10, 2021

#### “Geometry of Kaleidocycles”

###### Shizuo Kaji, professor (Institute of Mathematics for Industry, Kyushu University )

Abstract: Kaleidocycles are Origami models of flexible polyhedra which exhibit an intriguing turning-around motion (have a look at the pictures at https://github.com/shizuo-kaji/Kaleidocycle). The study of Kaleidocycles involves kaleidoscopic aspects and lies at the intersection of geometry, topology, and integrable systems (and mechanics). In this talk, we discuss two "incarnations" of them. (1) The states of a Kaleidocyce form a real-algebraic variety defined by a system of quadratic equations. In particular, the degree-of-freedom of its motion corresponds to the dimension of the variety. Using this formulation, we introduce a special family of Kaleidocycles, which we call the Mobius Kaleidocycles, having a single-degree-of-freedom (joint work with J. Schoenke at OIST). (2) A Kaleidocycle can be viewed as a discrete space curve with a constant torsion. Its motion corresponds to a deformation of the curve. Through this correspondence, we describe particular motions of Kaleidocycles using semi-discrete integrable systems (joint work with K. Kajiwara and H. Park at Kyushu University).

8:50 pm in Zoom | Register at http://bit.ly/MathWithoutBorders,Wednesday, March 10, 2021

#### Closing Remarks

###### Yuliy Baryshnikov, professor (University of Illinois Urbana-Champaign, Department of Mathematics)

Abstract: Closing remarks for the two-day workshop, Kyushu-Illinois Strategic Partnership Colloquia Series, "Mathematics Without Borders – Applied and Applicable."