Speaker: Ali Maalaoui (MIT)Title: The Conformal Fractional Dirac Operator and the Fractional Spinorial Yamabe problem.Abstract:I will first discuss the classical Spinorial Yamabe problem and its geometric relevance. Then I will review the construction of conformally invariant powers of the Dirac operator. I will focus in particular on the Caffarelli and Silvestre type extension and the renormalized energy expansion in the fractional setting. I will also address the construction of a Q-curvature operator in the critical case emphasizing the similarities with the case of differential forms.

Speaker: Elijah Bodish (MIT)Title: Spin link homologyAbstract: I will explain how folding can be applied to Khovanov-Rozansky’s $SL(2n)$ homology to give a new approach to categorifying the Spin$(2n + 1)$ Reshetikhin-Turaev link polynomial. To develop this new approach I will mention: skew Howe duality, categorical braid group actions, and i-quantum groups. This is based on joint work with B.Elias and D.Rose (arXiv:2407.00189).

Please join us on Wednesday, February 26, 2025 for the Pierce Seminar at 4 PM in Room 1-390 with Prof. Nam-Joon Cho.Abstract Title: Beyond the Circular Economy: Preparing for Tomorrow with Materials TodayAbstract:Throughout history, new materials have been the foundation of disruptive technologies. From bronze, paper, and ceramics to steel, polymers, and semiconductors, each material enabled far-reaching advances and defined the era. Seventy years ago, the synthesis of pure semiconductors as single crystals led to a complete transformation of the electronics industry and sweeping changes in communications, computing, and transportation. Today, inspired by the United Nation’s Sustainable Development Goals (SDGs) – a blueprint to achieve a better and more sustainable future for all – another new class of materials is emerging—one with both the potential to alleviate environmental burden, provide radically new functions, and to challenge our notion of what constitutes a “material.” These materials, inspired and co-opted from biology, combine (1) hybrid-composite design, combining disparate building blocks; (2) compartmentalized architecture, encapsulating desirable biomolecules while excluding others; and (3) hierarchical organization.Together, they enable unique and remarkable combinations of properties, including adaptability, plasticity, multi-functionality, and environmental responsiveness – far beyond those achieved by monolithic materials of the synthetic world. An extraordinary example is pollen, a discrete mesoscale compartment, which encapsulates, protects, and transports male genetic material in flowering plants enabling the biological imperative of reproduction. In this talk, I will introduce our ongoing efforts to explore the materials science of pollen and to transform pollen into a valuable commodity to produce pollen-based materials innovation as a sustainable solution to numerous outstanding environmental challenges. Key examples that will be covered include digital printing of shape-morphing materials, recyclable and reusable paper, and oil-absorbing sponges.Bio:Professor Nam-Joon Cho is a leading scholar of material science and infectious disease medicine. He pioneered new fields in sustainability and healthcare: from antiviral peptide technology to develop broad-spectrum drugs responding to COVID-19, to transformation of plant pollen to replace environmentally harmful plastics.Dr. Cho initiated a new paradigm for sustainability called “Cross Economy” which designs to create new industrial opportunities through material innovation including using the wastes. He works closely with healthcare companies and other industrial partners in these translational projects, including serving as Project Lead at Stanford University’s Antiviral Drug Discovery Centre for Pathogens of Pandemic Concern, where he spearheads collaborative research funded by the US National Institutes of Health. A pioneer in developing a new economic model for economic prosperity in hybrid worlds, he has received international honours from organisations such as the American Liver Foundation and Ministry of Science and ICT in South Korea. He is a member of the National Academy of Engineering of Korea.His research efforts have resulted in over 290 scientific papers in top journals such as Nature Materials, Nature Medicine, Nature Communications, Nature Protocols, Nature Human Behaviour, Science Translational Medicine, and Science Advances. The technology from his research group has been licensed and spun out to biotech companies with over S$26,000,000 in investment funding.Dr. Cho is also a passionate educator and mentor who has played leadership roles in the NTU Renaissance Engineering Programme, developed youth science education programs together with the United Nations and World Economic Forum, created international undergraduate research programs and joint graduate degree programs with leading university partners, and had group alumni become tenure-track faculty members and entrepreneurs worldwide. In addition, he currently serves as President of the Korean Scientist and Engineers Association in Singapore, is a member of the National Academy of Engineering of Korea. Earlier in his career, he was awarded the Nanyang Associate Professorship and Singapore National Research Foundation Fellowship.He is a graduate of Stanford University and the University of California, Berkeley.

Speaker: Yair Shenfeld (Brown University)Title: The Brownian and Poisson transport mapsAbstract:Transport maps serve as a powerful tool to transfer information from source to target measures. However, this transfer of information is possible only if the transport map is sufficiently regular, which is often difficult to show. I will explain how taking the source measure to be an infinite-dimensional measure, and building transport maps based on stochastic processes, solves some of these challenges both in the continuous and discrete settings.*Note change in date/location.

Speaker: Nick Early - IASTitle: Combinatorial Adventures in Configuration SpaceAbstract: In recent years, a surge of activity has uncovered deep connections between combinatorics, algebraic and tropical geometry, and scattering amplitudes in quantum field theory (QFT). In this talk, I will explain how these ideas naturally build on one another, unveiling new results and open problems in geometric combinatorics. Along the way, I will highlight several rich combinatorial structures that arise, involving the positive Grassmannian and configuration space, matroid subdivisions, and tropical hyperplane arrangements.

As part of MIT's Day of Climate, this professional development session provides training for the Climate Change Charades activity.Focused on elementary school-aged learners, climate change charades will address the gap in accessible, engaging, and interactive climate education.Learners act out or describe climate change-related concepts, helping to reinforce their understanding in a fun, collaborative way. Inspired by Climate Fresk workshops, which break down the complexities of the Intergovernmental Panel on Climate Change reports, this activity will utilize a similar concept to make learning about climate change more accessible.By acting out different environmental and climate phenomena, students will deepen their comprehension of key climate concepts while also building communication and teamwork skills. The interactive play allows for the responsible introduction of potentially climate-anxiety inducing topics to impressionable ages. This game can be used as an icebreaker, an introduction to more advanced topics, or a way to reinforce content already covered in class.Register for this in-person session.