MenuEvents for 02/25/2022 from all calendars
Working Seminar on Banach and Metric Spaces
Time: 10:00AM - 11:30AM
Location: BLOC 302
Speaker: Garett Tresch, Texas A&M University
Title: Schlumprecht space II
Mathematical Physics and Harmonic Analysis Seminar
Time: 1:50PM - 2:50PM
Location: BLOC 302
Speaker: Frank Sottile, TAMU
Title: Toric compactifications and discrete periodic operators
Abstract: Toroidal compactifications of Bloch varieties and Fermi surfaces for operators on discrete periodic graphs were used explicitly in the 1990's and implicitly recently. In this work, the graphs all had a similar (but common and important) structure. The theoretical foundations for toroidal compactifications---toric varieties has advanced considerably since the 1990's, including their structures as real algebraic varieties. I will explain how to associate a pair of projective toric varieties to any discrete periodic graph G such that the Bloch variety and Fermi surfaces of any operator on G are naturally hypersurfaces in these toric varieties. Not only does this provide a uniform construction of compactifications, but these toric varieties naturally admit a non-standard algebraic anti-holomorphic involution. When the operator is self-adjoint, the Bloch variety and Fermi surfaces become real algebraic hypersurfaces in their ambient non-standard real toric variety.
Noncommutative Geometry Seminar
Time: 2:00PM - 3:00PM
Location: ZOOM
Speaker: Ralph Kaufmann, Purdue University
Title: Noncommutative geometry in Hochschild complexes
Abstract: The fact that Hochschild cochain complexes are not commutative, but only commutative up to a controlled homotopy was a fundamental insight of Gerstenhaber.There is moreover a series of higher operations that can be neatly organized into an operadic structure, which is the content of Deligne’s conjecture.There is a whole package of operations on the chain level based on surfaces with extra structure, which we gave in 2006.In the case of a Frobenius algebra this yields a homotoy BV structure that essentially captures a circle action. In geometric situations this captures algebraic string topology operations, for instance an operation corresponding to the Goresky-Hingston coproduct. In newer work with M. Rivera and Zhengfang Wang, we extend these operations to Hochschild chain complexes and the Tate Hochschild complex,which connects the chain and cochain complexes and plays a role in singularity theory. There is a particular dualization which dualizes a higher multiplication found in this complex toa double Poisson bracket. These operations are natural from the point of view of surfaces and also allow for animation in the sense of Nest and Tsygan.
URL: Event link
Time: 4:00PM - 5:00PM
Location: BLOC 117
Speaker: Chris Bishop
Mathematical Biology Seminar
Time: 4:00PM - 5:00PM
Location: BLOC 302
Speaker: Goong Chen, Texas A&M University
Title: Modes of Motion of a Coronavirus
Abstract: In this talk, we study coronavirus from a structural molecular biology point of view, with certain emphasis on how the mechanical motions of the coronavirus may play in the invasion process of healthy cells. We first give a brief introduction and survey of the biological properties of a coronavirus concerning how it moves and how it invades healthy cells. The existing models of a coronavirus are mostly built atom-by-atom by microbiologists, to the best of our knowledge. A major finding by those researchers is the "wiggling" motion by the spikes of the virus. Such wiggling motion has been identified to play the important functions of browsing, surfing, and exploring activities in the virus' search and roaming to find healthy cells to invade. A single coronavirus contains hundreds of millions or even billions of atoms. Therefore, we can build our model by continuum mechanics in lieu of a mass-spring-dashpot atom-by-atom model. A spherical shell with many spikes mimicking the shape of coronavirus has been chosen as the elasto-plastic continuum. For this small continuum, we can analyze its eigenmodes of vibration by Modal Analysis. We have found the null space of six zero-frequency modes as translations (along three coordinate axes) and rotations (pitch, roll and yaw) and then, in addition, several thousands more nontrivial modes. They include the wiggling motion, and many other more peculiar modal shapes such as twisting, compression, embracing, locking, punching, and shaking-off actions. We also include the modal analysis of an IgG antibody. We make some hypothetical opinions regarding how a coronavirus may interact with an antibody based on their modal analysis. Many animation videos from supercomputer computations and simulations will be shown to illustrate the motions of a coronavirus.
