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Qualifying Exam

Title:  Non-Vanishing Homology of the Matching Complex

Abstract: A matching on a graph G is any subgraph where the maximum vertex degree is 1.  Since edge-deletion preserves the property of being a matching, the set of all matchings on G forms a simplicial complex M(G).  We will survey results on the lowest non-vanishing homology group for M(K_n) and discuss the extension of these results to more general graphs, specifically the r-stable ones.  Prior familiarity with simplicial complexes and homology is assumed.

Date:
-
Location:
745 Patterson Office Tower
Event Series:

Physics and Astronomy Colloquium: The Rainbow, the Rowland Circle, and other Geometric Adventures in Flat Space

The word "geometry" invokes imagery of curved space and singularities to physicists, warp drives and worm holes to physics enthusiasts, and Euclidean Dementors to middle-schoolers. But geometry (the structure of space) is at the heart of all physics, even in plain flat space. This talk is a series of three loosely-connected vignettes aspiring to illustrate the ubiquity of geometry in understanding our local environment.

Refreshments will be served in CP 179 at 3:15 PM

Date:
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Location:
CP155

Astro Seminar: Evidence for New relations between Gamma Ray Bursts Prompt and X-ray Afterglow Emission from 10 Years of Swift

Gamma-Ray Bursts (GRBs) are the most energetic transient events in the Universe.
Not only do they represent the violent end of a massive star and the birth of
a black hole, but their explosions allows us to trace them throughout the
entire Universe. With the launch of the NASA Swift Gamma-Ray Burst Explorer
Mission our knowledge of GRBs has been revolutionized. With its fast slew
capacity it is able to be on the position of a GRB within a minute or two after
the GRB is detected, giving us access to the earliest phases of a GRB afterglow.
Since its launch in November 2004, Swift has discovered more than 900 bursts,
about 280 with spectroscopic redshift measurements - providing us the
largest sample in history with prompt and afterglow observations. This unique
sample enables us to perform unprecedented statistical studies of GRBs.
In my talk I will review the history of GRB discoveries and their importance to
astrophysics. I will present the Swift mission and explain what is unique and
exciting about it and how Swift has given us new evidence for
connections between the GRB prompt and afterglow emission. The fate of the
burst is already determined during the explosion of the star.
I will finish the talk by looking into the future and explain how we can use
predictive data mining tools to determine the afterglow light curves and the
redshifts of the bursts based on observed properties of the burst.

The talk is primarily based on results published in
Grupe et al., 2013, ApJS, 209, 20

Date:
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Location:
CP171

Condensed Matter Seminar: Transport and Surface Potential Characterizations of Metal Oxides: Understanding Interplay among Charges, Surface Plasmons, and Photons

Metal oxides exhibit intriguing physical phenomena, including superconductivity, ferroelectricity, magnetism, metal-to-insulator transitions, resistive switching, catalytic activity, and sensing. While the band theory well explains the metals and semiconductors, intensive research efforts are still necessary to establish theoretical backgrounds for the electronic structures and transport properties of metal oxides. In particular, the surface and interface of the metal oxide, where periodic structures are truncated, can show peculiar electrical, magnetic, and optical properties quite distinct from those of the bulk counterparts. The underlying mechanism has been attributed to the strong interaction among charge, spin, orbital, and lattice at the surface and interface of the metal oxide. 
In this talk, I will introduce some of the recent research activities in my group – simultaneous measurements of surface work function (WS) and conductivity of metal oxide heterostructures. A Kelvin probe force microscopy (KPFM) system, equipped with a glove box and a variable temperature stage, enables us to measure WS of the sample. Heterointerface of LaAlO3 and SrTiO3, where two dimensional electron gas (2DEG) phenomena occur, shows close relationship between surface potential and interfacial conductance, under local electrical stress, ambient gas change, and light illumination, clearly revealing the strong surface-and-interface coupling. Nearly grain-boundary-free VO2/TiO2 thin films allow us to observe metallic and insulating domains with distinct WS values while varying the sample temperature. The percolation model well explains the evolution of the domain distribution and resistance during the metal-insulator transition of the VO2 thin films. ZnO/Ag nanogratings show significantly enhanced photoluminescence with the help of surface plasmon polaritons (SPPs). KPFM measurements reveal how SPP excitation influences surface photovoltage of the nanograting. All these results suggest that surface work function measurements using KPFM are very useful to unveiling origins of fascinating physical properties of metal oxide heterostructures.
Date:
-
Location:
CP179

Discrete CATS Seminar

Title: An Introduction to Symmetric Functions, part II

 

Abstract: In this pair of talks, I will provide an overview of basic results regarding symmetric functions.  My goal will be to create a "road map" for anyone who is interested in reading more about these objects in Chapter 7 of Stanley's Enumerative Combinatorics, Volume 2 (if you have a copy and are interested, it might be helpful to bring it with you).  We will motivate the study of symmetric functions by interpreting them as generalizations of subsets and multisubsets of [n], so these talks should be accessible to anyone who is familiar with the material from the first part of MA 614.

Date:
-
Location:
745 Patterson Office Tower
Event Series:
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