Speaker: Asaf Hadari (U. Hawai`i)
Title: Polynomial equations with varying exponents.
Abstract: There is a rich and classical theory concerning the following question: how do the roots of a polynomial vary when you vary its coefficients? I’d like to talk about a surprisingly unexplored related question: how do the roots of a polynomial vary when you freeze its coefficients, but vary the exponents?
I’ll give some examples where this question turns out to be important (some from 3-manifold theory and some from graph theory), discuss what questions might be natural to ask about the roots, and then answer the questions.
Speaker: Prof. David Hu (Georgia Tech)
Title: Assembly of rafts and towers by ants
AbstractFire ants are excellent model organisms for studying active self-healing materials. By linking their legs together, they build highly interconnected networks that can quickly rearrange themselves in response to applied stress. In this talk, we present experiments and modeling that elucidate their construction. Spherical rafts of ants morph into pancakes within minutes; towers are constructed to provide an equal compressive load on each ant. We also use plate-on-plate rheology to show ants modify their elastic and viscous moduli by rearrangement of their bodies. At the end of the talk, we present our outreach work on the Law of Urination, stating that animals from cats to elephants empty their bladders over the same duration of 21 seconds.
Biography: Dr. David Hu is a mechanical engineer who studies the movement of animals. He has studied how snakes slither, how insects walk on water, and how small insects fly through rain. His laboratory has invented new animal-like robots such as Robostrider which walks on water and Scalybot, which moves by virtue of its belly scales. He lives in Atlanta with his wife Jia and children, Harry and Heidi.
Hu is an Assistant Professor of Mechanical Engineering and Biology and Adjunct Professor of Physics at Georgia Institute of Technology. His degrees are in mechanical engineering and mathematics at M.I.T. and his postdoctoral work was at NYU. He has published in Nature, PNAS, Physics Today and American Scientist, and his work been featured in The Economist, The New York Times, The Washington Post, USA Today, National Geographic, Popular Mechanics, Audobon, Smithsonian, Scholastic, and others. He has been invited guest on Good Morning America, Discovery Channel, National Public Radio, and in the film Fire Ants 3D: The Invincible Army, available on NetFlix. These videos and more may be found at his website, Hoogle at http://www.me.gatech.edu/hu/
Speaker:Charlie Micchelli (U. Albany)
Title: A Fourier analysis to identifying the limit of “flat” interpolation by radial basis functions approach.
Abstract: Following the work of several authors we are led to consider the limit of RBF interpolation when both the centers of the RBF and the argument of the interpolant simultaneously go to zero. In this talk, we refine and approach that was used about forty years ago in the study of stability of difference methods with least local truncation error for parabolic equations and provide general conditions on the Fourier transform of the RBF which allows for the precise description of the limit of “Flat” RBF interpolation.
Title: Surreal numbers and nonstandard analysis: foundations of
infinitesimal calculus.
Speaker: Vladimir Kanovei
Inst. for the Information Transmission Problems of RAS, and
Moscow State University of Railway Engineering (MIIT) (Moscow)
Abstract: A system of foundations of infinitesimal calculus will be proposed and
discussed.
The system is based on two class-size models, including
1) the surreal numbers, and
2) the Kanovei-Shelah set-size-saturated limit ultrapower model.
Some historical remarks will be made, and some related problems will be
discussed, too.
Title: Surreal numbers and nonstandard analysis: foundations of
infinitesimal calculus.
Speaker: Vladimir Kanovei
Inst. for the Information Transmission Problems of RAS, and
Moscow State University of Railway Engineering (MIIT) (Moscow)
Abstract: A system of foundations of infinitesimal calculus will be proposed and
discussed.
The system is based on two class-size models, including
1) the surreal numbers, and
2) the Kanovei-Shelah set-size-saturated limit ultrapower model.
Some historical remarks will be made, and some related problems will be
discussed, too.