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  • OTHER MATHEMATICS DEPARTMENT EVENTS

    OTHER MATHEMATICS DEPARTMENT EVENTS
    Mathematics for Human Flourishing: Francis Su

    4:30 PM-6:00 PM
    October 6, 2022

    Math is more than just a way to describe the world, and it is more than just a set of skills, like doing arithmetic and factoring a quadratic. Math is a deeply human enterprise that fulfills basic human longings, such as for beauty and truth. When properly engaged, it builds virtues like persistence, creativity, and a competence to solve new problems. These virtues will serve you well no matter what you do in life. It was an incarcerated man–now his friend–that helped distinguished mathematician Francis Su see this more clearly than ever before.

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  • OTHER MATHEMATICS DEPARTMENT EVENTS

    OTHER MATHEMATICS DEPARTMENT EVENTS
    Jameel Al-Aidroos Mathematical Pedagogy Lecture Series

    3:00 PM-6:00 PM
    October 17, 2022
    1 Oxford Street, Cambridge, MA 02138 USA

    Jameel Al-Aidroos was a treasured colleague and a master of a myriad of things. He could simplify a mathematical idea and present a question or comment in a way that could bring his students to view concepts from new perspectives. Likewise, when he worked with graduate students around pedagogy and with school teachers around the joys of engaging with mathematics, the thoughtful way he approached teaching and mentorship made a big difference. Watching Jameel teach motivated and inspired both novice and veteran teachers to become better instructors and to bring their best selves forward. His superpower as a teacher was asking just the right questions to focus students’ attention on the core of the mathematical idea.

    Through a number of seminars and workshops, Jameel shared his question-asking approach and pedagogical skills with graduate students and faculty. An astute and careful listener, a masterful communicator, and a deep thinker, he forged impactful connections. As a mentor and colleague, Jameel was without equal: he applied himself wholeheartedly to hone his craft in the classroom and as a mentor. He was quick to volunteer to do whatever was needed to promote team projects and through this, we discovered his enormous talents as an interviewer, film editor, and voice-over artist, among other things. It seemed there were no tasks he did not choose to rise to and polish, while consistently taking a step out of the limelight to let his students and colleagues shine.

    The grace and generosity of spirit he extended to his students and colleagues are an indelible part of his legacy. Jameel carried this grace and generosity throughout his long battle with cancer. We honor his contributions and dedication to teaching and learning at Harvard via this speaker series as a small way to remember Jameel’s extraordinary warmth of character and pedagogical skills. He motivated and inspired his students and colleagues; through this series, we hope to celebrate and keep alive that legacy by bringing speakers who share new perspectives on mathematics and pedagogy, and motivate us to reflect on our professional roles.

    Jameel Al-Aidroos Mathematical Pedagogy Lecture Series

    When: October 17, 2022

    Where: Hall E, Science Center, 1 Oxford Street, Cambridge, MA, 02138

    Register for the In-Person Event.

    Register for the Online Event.

    Download a detailed PDF schedule of lectures and events.

    Schedule
    3 p.m. – 3:50 p.m.

    Aubrey Clayton | Author of Bernoulli’s Fallacy: Statistical Illogic and the Crisis of Modern Science

    Thinking Slowly about Probability and Statistics

    3:50 p.m. – 4 p.m.

    Break

    4 p.m. – 4:50 p.m.

    Juliana Belding | Associate Professor of the Practice of Mathematics at Boston College

    Working with Secondary Math Teachers: What Mathematicians can Offer and Learn

    5 p.m. – 6 p.m.

    Refreshments in The Austine & Chilton McDonnell Common Room, Science Center 4th floor.

     

    Organizers

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  • CMSA EVENT: CMSA Topological Quantum Matter Seminar: Kähler bands—Chern insulators, holomorphicity and induced quantum geometry
    9:00 AM-10:00 AM
    October 26, 2022
    1 Oxford Street, Cambridge, MA 02138 USA

    The notion of topological phases has dramatically changed our understanding of insulators. There is much to learn about a band insulator beyond the assertion that it has a gap separating the valence bands from the conduction bands. In the particular case of two dimensions, the occupied bands may have a nontrivial topological twist determining what is called a Chern insulator. This topological twist is not just a mathematical observation, it has observable consequences—the transverse Hall conductivity is quantized and proportional to the 1st Chern number of the vector bundle of occupied states over the Brillouin zone. Finer properties of band insulators refer not just to the topology, but also to their geometry. Of particular interest is the momentum-space quantum metric and the Berry curvature. The latter is the curvature of a connection on the vector bundle of occupied states. The study of the geometry of band insulators can also be used to probe whether the material may host stable fractional topological phases. In particular, for a Chern band to have an algebra of projected density operators which is isomorphic to the W∞ algebra found by Girvin, MacDonald and Platzman—the GMP algebra—in the context of the fractional quantum Hall effect, certain geometric constrains, associated with the holomorphic character of the Bloch wave functions, are naturally found and they enforce a compatibility relation between the quantum metric and the Berry curvature of the band. The Brillouin zone is then endowed with a Kähler structure which, in this case, is also translation-invariant (flat). Motivated by the above, we will provide an overview of the geometry of Chern insulators from the perspective of Kähler geometry, introducing the notion of a  Kähler band which shares properties with the well-known ideal case of the lowest Landau level. Furthermore, we will provide a prescription, borrowing ideas from geometric quantization, to generate a flat Kähler band in some appropriate asymptotic limit. Such flat Kähler bands are potential candidates to host and realize fractional Chern insulating phases. Using geometric quantization arguments, we then provide a natural generalization of the theory to all even dimensions.


     

  • NUMBER THEORY SEMINAR
    3:00 PM-4:00 PM
    October 26, 2022
    1 Oxford Street, Cambridge, MA 02138 USA

    The usual language of algebraic geometry is not appropriate for arithmetical geometry: addition is singular at the real prime. We developed two languages that overcome this problem: one replace s rings by the collection of “vectors” or by bi-operads, and another based on “matrices” or props. Once one understands the delicate commutativity condition one can proceed following Grothendieck’s footsteps exactly. The props, when viewed up to conjugation, give us new commutative rings with Frobenius endomorphisms.


     

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