Talks in the Department of Mathematical Sciences (Fall 2007)

• Dept. of Mathematical Sciences Seminar
  Dr. John W. Kennedy, Mathematics Department, Queens College, CUNY
  Wednesday, November 28, 2:45-3:45 pm in Room RI-106
  
  Title: Leonhard Euler Was Not Really A Graph Theorist - Or Was He?
  Abstract: During the year 300 A.E. we have probably had many chances to celebrate the mathematics gifts from Leonhard Euler. Although Euler was not officially a graph theorist - graph theory had not been "invented" in his time - his gifts were incorporated into the development of the subject. Indeed, Euler is credited with the first ever "theorem in graph theory" (1736). In this seminar I will explore Euler's gifts to graph theory from a perspective that is perhaps unique to my own interests in the subject. An in-depth background in graph theory is not a prerequisite for participation in this seminar that will "connect some dots" in linking Euler's graph theory gifts with presents from such other personalities as Plato, Hamilton, Gauss, Kurotowski, and Guthrie (Francis not Woody or Arlo).
  
  
• Dept. of Mathematical Sciences Seminar
  Dr. Jonathan Cutler, MSU
  Wednesday, November 14, 2:45-3:45 pm in Room RI-222
  
  Title: Trees through specified vertices
  Abstract: In this talk, we present a result which proves a conjecture of Horak, which can be said to be related to classical theorems in graph theory including Dirac's theorem. A. We will present a proof of a special case of this theorem along with some related open questions.
  
  
• Dept. of Mathematical Sciences Seminar
  Jun Zhang, New York University
  Thursday, October 25, 4:00-5:00 pm in Room RI-222
  
  Title: Free-moving boundaries interacting with thermal convective fluids
  Abstract: Thermal convection has come to be regarded as one of the most important prototypical systems of dynamical systems. It has been extensively studied over the past 3 decades or so. An experimental system often consists of a fluid confined within a rigid box that is heated at the bottom and cooled at the top.
  
  Our experimental studies explore the intriguing phenomena when its rigid boundary is partly replaced either by a freely moving, thermally opaque (which reduces local heat transport) "floater" or by a collection of free-rolling spheres (a deformable mass). We identify from our table-top experiments several dynamical states, ranging from oscillation to localization to intermittency. A phenomenological, low-dimensional model seems to reproduce most of the experimental results. Through our on-going experiments, we further seek their possible implications in geophysical processes such as continental drift.
  
  
• Dept. of Mathematical Sciences Seminar
  Tamara Kucherenko, University of California, Los Angeles (UCLA)
  Wednesday, September 19, 12:00-1:00 pm in Room RI-222
  
  Title: Absolute functional calculus for sectorial operators
  Abstract: We introduce absolute functional calculus for sectorial operators, which is stronger than H -calculus. Using this technique, we prove a theorem of Dore-Venni type for sums of closed operators. There, we are able to remove any assumptions such as R-boundedness or BIP on one of the operators given that the second operator has absolute calculus. Moreover, we show that any sectorial operator has absolute calculus on the real interpolation spaces between the domains of its fractional powers. As an application we obtain results regarding the well-posedness and existence of mild solutions to the Cauchy problem on Holder and Besov spaces. (Joint work with N. Kalton.)