The Department of Physics and University College will again sponsor a series of public lectures, to be held at 10 a.m. on Saturday mornings, April 7th – April 21st. Due to campus construction, all lectures will be held in McMillan G052. This building is directly across from the parking garage off Forest Park Parkway; parking is free on Saturdays. These lectures, which are free and open to the public, will be presented by faculty members of the Department of Physics and are tailored for the general public. More information may be obtained from Ady Haas at 935-6276.

### Spring 2018: Magnetic Monopoles, Vortices and Topological Order: Physics and Mathematics Reunite

The 2016 Nobel Prize in Physics was awarded to David J. Thouless, F. Duncan M. Haldane and J. Michael Kosterlitz "for theoretical discoveries of topological phase transitions and topological phases of matter”. Topology, a branch of modern mathematics, is concerned with properties of objects that don’t change under stretching and shrinking. The incorporation of ideas from topology over the last few decades has had a tremendous impact on modern physics. Many of the exotic objects of modern physics are topological in character, from cosmic strings and wormholes in astrophysics to magnetic vortices and topological insulators in condensed matter physics. Just as calculus was Newton’s tool in setting the foundations of classical physics, topology is an essential tool today in modern theoretical physics. We will explore the research that won the 2016 Nobel prize as well as related ideas in modern physics.

**From wormholes to monopoles- an introduction to topology in physics**
Topology snuck into physics in 1931 when Dirac introduced the concept of magnetic monopoles, and showed that their existence would explain quantization of electric charge. Wormholes in space and time were first proposed by Weyl in 1928, but the term itself was introduced by Wheeler and Misner in 1957. However, the active study of topology in mainstream physics only began in the 1970’s. We will explore some of the basic ideas of topology in physics, using examples from everyday life as well as modern physics.

**Topological defects and phase transitions**
We are all familiar with phase transitions between different states of matter. On increasing the temperature (and/or external pressure), ice transforms into water and melts. However, what is "melting" microscopically? Precisely these sorts of very basic and important questions have occupied many physicists. In turns out that most "melting" transitions are associated with the proliferation of "topological defects". These topological defects are all around us. There are "dislocations" or "disclinations" in crystals (playing a crucial role in work hardening of steel), "domain walls" as well as "monopole" type excitations in magnets of various types, and whirlpool like "vortices" in superconductors and superfluids. In typical "melting" transitions, these topological defects multiply and ultimately eradicate crystalline type order. Our current understanding of most phase transitions and much of the talk will be devoted to an explanation of the notion of "parameters" characterizing crystalline or other "orders" and the topological defects that perturb them. We will discuss the interplay between energy and entropy in phase transitions. We will then turn to discuss intriguing cases in which "melting transitions" exist even when no true ("crystalline" like) ordered states appear at low temperatures; the 2016 Nobel Prize in physics recognized the first such found "topological transition" in two dimensional systems.

**Topological phases of matter**
Solid, liquid, gas, these are the phases of matter known to most of us from school. Many more distinctions are, however, known to condensed matter physics, which classifies materials into a great host of different phases or “states” of matter. For example, a metallic conductor and an insulating material are thought to be in different states of matter, even if they are both solid materials. Unlike water or ice, some of these states of matter lend remarkable stability to certain physical properties, such as conductance. These are known as "topological phases”. The 2016 Nobel Prize was in part awarded for groundbreaking insights into how topology, the field of mathematics that explores stable properties of geometric shapes, can also explain stable properties of certain phases of matter. Recent developments along those lines include the celebrated ``topological insulators’’, materials that are electrically insulating on the inside but are metallic on their surface. We will review the pieces of topology, electromagnetism, and quantum physics that conspire to give rise to these fascinating behaviors.

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