Susanne Reffert MY STUDIES. Theoretical/Mathematical Physicist. Many connections between mathematics and physics!

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1 Susanne Reffert MY STUDIES Theoretical/Mathematical Physicist Many connections between mathematics and physics!

2 Susanne Reffert born in Zürich, Switzerland German nationality

3 High School always wanted to be a scientist age 13-19: classical high school (Latin is a main subject) favorite subject: chemistry chemistry kit (experiments) growing crystals at home CuSO4 Alum (KAl(SO4)2)

4 High School Biology Camp (Biozentrum Basel): growing protein (lysozyme) crystals Supercomputing Camp (Swiss National Supercomputing Center)

5 Useful computer skills: UNIX/Linux MATLAB, Maple, Mathematica Programming: C, C++ LaTeX High School

6 Sierpinski Triangle High School Fractals Mandelbrot set

7 High School Read a lot of books: molecules, particle accelerators, fractals, astronomy, cosmology etc.

8 High School Research Project: Computer program that composes Baroque melodies using random numbers and a set of rules Participated in national and European science competitions Many different interests, hard to choose!

9 High School: Useful Lessons Curiosity is the most important trait of a scientist: How do things work? How do natural phenomena come about? You must be very interested/motivated to succeed. Good grades in school are not determining factor. Look around and try out different subjects to find what suits you best. Look at things beyond high school level science ( real life science is very different).

10 University Studies Physics, as the most fundamental of the natural sciences first 2 years together with mathematicians preference for theoretical physics interest in particle physics first 2 years common for everyone start specializing in 4th year diploma thesis ~ 5 years in total

11 University Studies What are the basic mathematical tools for the physicist? calculus (differentiation integration,...) linear algebra (vectors, matrices, systems of lin. equations...) mathematical methods: Fourier analysis, distributions, harmonic analysis complex analysis Advanced topics: differential geometry (General Theory of Relativity) functional analysis (Quantum Mechanics) group theory and representation theory (gauge theories etc.) Mathematics gives a set of tools to the physicist use mathematics for physics calculations less rigorous, more goal-oriented (no proofs, but applications)

12 The 4 Fundamental Forces Electromagnetic Force carrier particle: photon

13 The 4 Fundamental Forces Weak Nuclear Force carrier particles: W+, W-, Z Strong Nuclear Force carrier particles: gluons

14 The 4 Fundamental Forces Gravitation carrier particle: graviton

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16 Search with particle accelerators Large Hadron Collider (LHC) CERN (Switzerland)

17 Unification Electromagnetic Force Weak Nuclear Force Strong Nuclear Force Standard Model of Particle Physics?????? Gravitation

18 String Theory point particle string

19 University Studies: Useful Lessons Most important: perseverance. Keep trying until you understand everything, don t be discouraged. Look around for a specialization that suits you. Read a lot. Consider changing university for graduate studies/go abroad. You never stop learning. What you learn during your undergraduate years is just the start.

20 PhD Thesis Prof. Dieter Lüst 3 years total publish a number of papers apply for postdoc position after 2 years write a thesis

21 PhD Thesis Before: you learn from lectures and textbooks Now: based on previous knowledge, you have to take the next step into the unknown. In research, the outcome it not clear. Test a new idea, test its implications, generalize an existing idea, etc. Different way of working. Curiosity again most important. Often frustrating (get stuck for months, ideas don t work) Good points: Travel to attend schools and conferences.

22 PhD Thesis: String Compactifications String Theory lives in 10 dimensions Since our world is 4-dimensional, we must get rid of the extra 6 dimensions Make them very small: compactification 6-dimensional compact space is a manifold -> study geometry of compact space to learn about properties of string theory (Calabi-Yau manifold, complex geometry, Kähler geometry, toric geometry, orbifolds) do mathematics to learn about physics

23 PhD Thesis: String Compactifications Easiest example: compactification on a sphere. Idea: wrap extra dimensions into a sphere and make it very small.

24 PhD Thesis: String Compactifications More difficult example: compactification on a 2-torus. Im(z) R /R 1sinθ τ=r /R e iθ Re(z)

25 PhD Thesis: String Compactifications Usually (much more difficult): Calabi-Yau manifold 6-dimensional section of Calabi-Yau

26 PhD Thesis: Useful Lessons Learn to think independently. Most important. Read a lot of papers to see what interests you most. Try pursuing your own ideas. Learn to work with others. In physics, collaborating is very important. Discuss with and learn from others (fellow students). Acquire a set of useful skills. Attend conferences. Hear about new subjects. Meet people. A strong network is important for collaborations and finding jobs. Give seminar talks. If you are very interested in finding a postdoc position in a certain group, visit there and give a talk.

27 What s next? Take up postdoctoral positions Move (change country/continent) every 2-3 years Hard to find postdoc positions (less positions than applicants) Often leads to difficult family situations (spouses living in different countries...) Research can be rather frustrating. Many people give up. Eventually find faculty position (professor, permanent position) Success is not guaranteed! Only recommended if you are very motivated. Many other possibilities outside academic world (banking, finance, consulting, insurances, etc.)

28 Prof. Robbert Dijkgraaf Postdoc

29 Postdoc Research: Dimers and Crystal Melting Relation between String Theory and models in statistical physics. Different mathematics needed: Graph theory Combinatorics (counting things) Cohomology Number Theory

30 Postdoc Research: Dimers and Crystal Melting Statistical system of a melting crystal corner. Obeys crystal melting rules.

31 Postdoc Research: Dimers and Crystal Melting Partition function is given by the MacMahon function: Z cr = 3d partitions q #boxes = n=1 1 (1 q n ) n q = e 1/T =1+ q+ q 2 + q 2 + q 2 + q

32 Postdoc Research: Dimers and Crystal Melting Graph G, nodes can be colored black and white such that back nodes are only joined by edges to white nodes and vice versa: bipartite. Let M be a subset of the set E of edges of G. M is called a matching, if its elements are links and no two of them are adjacent. If every vertex of G is saturated under M: perfect matching. Link which joins a black and a white vertex: dimer.

33 Postdoc Research: Dimers and Crystal Melting Dimer model on hexagonal lattice: empty room 1 plaquette flip rhombus tiling Another description of melting crystal!

34 Postdoc Research: Dimers and Crystal Melting Different description: vicious walkers - random walkers whose paths must not intersect.

35 Postdoc Research: Dimers and Crystal Melting Study the lower dimensional analog: 2d partitions Integer partition: e.g. 6=3+2+1 Z 2d = 2d partitions q #squares = n=1 1 1 q n

36 Postdoc Research: Dimers and Crystal Melting black point white point ψ 1 2 Black dots can hop to a free neighboring place: spin chain

37 Postdoc Research: Dimers and Crystal Melting Moving black dots is the same as adding and removing squares! Also this system has many different descriptions.

38 Postdoc

39 Postdoc Research: Useful Lessons You re on your own now. Try to learn a new subject/change direction. Try to learn something new from each research project.????

40 Thank you for your attention!