פעילויות השבוע

גרפים מרחיבים הם בעלי שימושים רבים במתמטיקה ובמדעי המחשב. בשנים האחרונות התחיל להתפתח תחום מחקר חדש שמנסה להכליל את הרעיון של גרף מרחיב לאובייקטים מממדים גבוהים יותר. ההרצאה תסקור חלק קטן מההתפתחות בתחום בשנים האחרונות

Let $V$ be a representation of a connected reductive group $G$. A representation is cofree if $k[V]$ is a free $k[V]^G$ module. There is a long history of work studying and classifying cofree representations of reductive groups. In this talk I present a simple conjectural characterization of cofree representations in terms of geometric invariant theory. Matt Satriano and I have proved the conjecture for irreducible representations of SL_n as well as for torus actions. I will give motiviation for the conjecture and explain the techniques which can be used for its verification. This talk based on joint work with Matt Satriano.

We will consider some basic optimization problems and how they relate to optics. We then define an index of refraction to any given distribution. We conjecture an estimate for the index and explain how its related to some natural operations research questions. We also consider lenses and ask questions about the probabilistic behavior of discrete geodesics in a lens setting.