(11 a.m. - 12 p.m.)

**Natasa Macura**

**Department of Mathematics**

**Trinity University**

**CAT(0) cube complexes with polynomial divergence of geodesics**

Divergence of geodesics is a property of a metric space that reflects its curvature: in Euclidean plane (flat) it is linear, and in the hyperbolic plane (negative curvature) it is exponential. Gersten was the first to describe examples of quadratic divergence in spaces of non-positive curvature, and he then posed a question if higher degree polynomial divergence is possible in such spaces.

I will describe examples of CAT(0) cube complexes with polynomial divergence of geodesics of degree greater than two, providing an affirmative answer to Gersten's question.

We will start with a brief summary of main ideas and approaches in geometric group theory, presenting the question and the result in the context of this vibrant area of mathematics.

I will then talk about CAT(0) spaces and groups that act on them, and will construct a family of finite 2-dimensional cube complexes whose universal covers are CAT(0), and have the polynomial divergence of geodesics of desired degree.

The talk is aimed as general mathematical audience, and knowledge of geometric group theory will not be assumed.

Coffee to be served at the classroom 30 minutes prior to the talk.

(1 p.m.)

All Faculty Are Invited to the Final Examination of

**Panikki Bandaralage Chandima Dhanuka Bandara Bulumulla**

Graduate Program in Chemistry

April 20, 2018, 1:00 p.m., FA 2.206

**Title of Dissertation:**

Non-Conventional Building Blocks for Organic Electronics

**Student’s Supervising Committee:**

Mihaela C. Stefan, Chair

Michael C. Biewer

John P. Ferraris

Yves J. Chabal

]]>(3 p.m.)

All Faculty Are Invited to the Final Examination of

**Edward Hooton**

Graduate Program in Mathematics

April 20, 2018, 3:00 p.m., GR 2.302

**Title of Dissertation:**

Existence and Stabilization of Periodic Solutions in Equivariant Systems

**Student’s Supervising Committee:**

Dmitrii Rachinskii, Co-Chair

Zalman Balanov, Co-Chair

Qingwen Hu

Wieslaw Krawcewicz

Vladimir Dragovic

]]>(3 p.m. - 4 p.m.)

Dr. Robert Cava (Princeton University)

The discovery of superconductivity, the transmission of electrical current with zero energy loss, recently passed its 100th anniversary. This truly remarkable property of matter, found at cryogenic temperatures, has made its way into a variety of important uses in modern society, but nature has not yet given us the ultimate practical material that will change the world through its lossless transmission of electrical energy over long distances. Research on this complex problem in materials science persists in the world at many levels, and progress is continuously made on both scientific and practical fronts, in spite of the impatience that is often displayed by both the scientific and lay public, who prefer more immediate gratification. In this talk I will briefly describe where we are in this field, and how we got here, and describe the vision that some have had for where we should be going. Because my personal research is in the discovery of new superconducting materials, only one facet among the larger set of fundamental and practical issues currently under study, the talk will concentrate somewhat in that area.

]]>(4 p.m. - 5 p.m.)

Dr. Robert Cava (Princeton University)

“New materials give new properties” is a phrase that I think best describes the goal of our research program. We find new materials by thinking about how the chemistry and structures of materials at the level of the atoms and the unit cell might determine the electronic and magnetic properties of matter. Although we are often wrong in our deductions, either failing altogether or finding new materials with conventional properties, our chemical perspective can sometimes lead to new materials that we hope will have properties of interest in materials physics. This process would be easier if there was a way to reliably proceed from predicting the stability of an unknown non-molecular solid, predicting what its properties will be, and then making and testing it, but that is not currently the case. By talking with experimental and theoretical physicists we learn about issues in the electronic and magnetic properties of matter that might be addressed through the introduction of new materials, and being in a chemistry department teaches us how to think about structure and bonding; our work is about putting the pieces together to get new materials of interest. In this talk I will describe some of our recent results in several new materials areas, ranging from new superconductors and geometrically frustrated magnets to Topological Insulators. Our research is supported by the US Department of Energy, the Gordon and Betty Moore Foundation, the Army Research Office, and the US National Science Foundation.

]]>(3 p.m. - 4:15 p.m.)

"Bioenergetic Dysfunction and Mitochondrial Cascades in Alzheimer's Disease"

Abstract: What initiates Alzheimer’s disease (AD) clinical and histology changes in those with late-onset AD (LOAD) is unclear. An association between advancing age, AD histology changes, and AD incidence suggests mitochondria and bioenergetic dysfunction may play a role or even initiate the disease. Brain energy metabolism and mitochondrial function change with advancing age and in AD, leading some to propose a “mitochondrial cascade hypothesis” in which bioenergetic changes are hypothesized to initiate AD histology and clinical decline. This presentation reviews AD-associated changes in brain energy metabolism, considers whether these changes may play a relatively upstream and important role in LOAD, and discusses whether targeting brain energy metabolism offers a reasonable and practical therapeutic strategy.

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