I studied mathematics and physics at the University of Bielefeld in Germany and hold a PhD in theoretical physics from the Ludwig Maximilian University of Munich, based on research carried out at the Max Planck Institute for Physics between 2008 and 2011. This work was continued at the Northeastern University in Boston, USA as an NSF-funded postdoctoral research associate. My research work in the area of string theory was focused on F-theory phenomenology and related mathematical questions.

  • 07/2011 – 09/2012: Postdoc Mathematical Physics
    Northeastern University 
  • 03/2011 – 07/2011: Postdoc Mathematical Physics
    Max Planck Institute for Physics 
  • 05/2008 – 02/2011: Physics PhD
    LMU Munich  and
    Max Planck Institute for Physics 
  • 10/2002 – 05/2008: Math diploma (= M.Sc.)
    10/2002 – 07/2007: Physics diploma (= M.Sc.)
    University of Bielefeld 

Background

Mathematical Physics

String theory is a branch of mathematical physics based upon the idea of one-dimensional fundamental objects, which are called strings. This approach of using extended objects takes care of many problems encountered in the point particle based description of nature via quantum field theories, e.g. the well-established Standard Model of Particle Physics. While mathematical self-consistency specifies certain parts of the theory almost uniquely, the dimensional compactification, which is necessary to make contact with our four-dimensional world, yields an entire landscape of possible vacua with no obvious method to point out the right one. Another issue is the fact that our current theoretical understanding of string theory itself is somewhat limited, as we only have an perturbative (i.e. “approximative”) understanding whereas the non-perturbative “full” theory still remains unknown…

Research Work

My research work in mathematical physics in 2012 was focused on understanding the geometric properties of the Large Volume Scenario and Swiss Cheese-type Calabi-Yau manifolds. A plan for the future was to spend a significant amount of (cloud) computing resources on related string landscape scans with the Boston collaboration. However, I left Boston before those attempts produced much results, we were just getting started after my first year was completed. Back then I was also very interested in modern constructions of Calabi-Yau 3-manifolds.

Before that, while working on my PhD in Munich, I was involved in F-theory GUT model building, which is a branch of non-perturbative string theory. This followed the developments in this area after a small “minirevolution” in early 2008. During the better part of 2010 and continuing in 2011 I worked on projects somewhat off the phenomenological main stream that focused on related mathematical methods, specifically the computation of cohomology group dimensions in toric settings, see the cohomCalg project below.

Note: Please note that I left academic employment in 2012 for an industry position. The material found here essentially refers to my active research work from 2006 to 2012.

Contributions

F-theory is a hypothesized theory, that can only be described indirectly via dualities. From a conservative perspective, F-theory is just a geometrization of a symmetry within perturbative type IIB string theory. On the other hand, it can be realized as a particular limit of the non-perturbative M-theory. A third description relates F-theory to the heterotic string. All of those indirect definitions are equally valid and highlight the intricate structure of interconnects and links between the various branches of string theory. Overall, F-theory offers an elegant perspective that unifies many non-perturbative aspects like instantons, 7-branes, geometry backreactions etc. The price, however, to work within the F-theory framework comes in the form of various technical and mathematical challenges—which makes this subject all the more interesting to me…

After some early failed attempts to get a better understanding of the strong-coupling regime of IIB orientifolds based on \((p,q)\) 7-branes and \(ABC\)-brane collections, it turned out that F-theory is indeed the right framework to discuss non-perturbative aspects of type IIB string theory. The work revealed a number of more or less surprising restrictions on the gauge group one can obtain in global F-theory models obtained from simple IIB uplifts. In a more involved investigation of the model building properties, the usage of the spectral cover description of the gauge flux allowed us to provide further details on the phenomenological issues in global F-theory GUT model building. In particular, we were able to find a rather simple global model having three chiral matter generations as an explicit example. In our next project we considered instantons, more precisely the uplift of D3-brane instantons in IIB-orientifolds with their supposed uplift counterparts, the M5-brane instantons.

Parallel to this project, we also investigated a new algorithm for computing the cohomology of line bundles on toric varieties, a task which appeared more and more often in our work on instantons. Considerable time was spend on a suitable implementation and subsequent questions arising from this project. During the work on direct applications of this algorithm in theoretical physics a generalization of the algorithm to equivariant geometries was conjectured. Ultimately, the algorithm and derivative results were both proven by our group and—surprisingly—by a completely unrelated colleague from mathematics.

Further reading: Back in 2010 and 2011 I wrote some elementary introductions to the subjects of string theory and F-theory in case you want to know more.

Publications

Mathematical Physics

INSPIRE-HEP database arXiv preprints

More than 420 citations in total. A reverse chronological list of publications from my academic research years in theoretical and mathematical physics:

  • “Calabi-Yau Manifolds with Large Volume Vacua” by James Gray, Yang-Hui He, Vishnu Jejjala, Benjamin Jurke, Brent D. Nelson and Joan Simón, Phys.Rev. D86 (2012) 101901, arXiv:1207.5801 [hep-th], 2012.

  • “Computing Cohomology on Toric Varieties” by Benjamin Jurke, Proc.Symp.Pure Math. 85 (2012) 391-400, arXiv:1109.1571 [math.AG], 2011.

  • “Computational Tools for Cohomology of Toric Varieties” by Ralph Blumenhagen, Benjamin Jurke and Thorsten Rahn, Adv.High Energy Phys. 2011 (2011) 152749, arXiv:1104.1187 [hep-th], 2011.

  • “Cohomology of Line Bundles: Applications” by Ralph Blumenhagen, Benjamin Jurke, Thorsten Rahn and Helmut Roschy, J.Math.Phys. 53 (2012) 012302, arXiv:1010.3717 [hep-th], 2010.

  • “Cohomology of Line Bundles: A Computational Algorithm” by Ralph Blumenhagen, Benjamin Jurke, Thorsten Rahn and Helmut Roschy, J.Math.Phys. 51 (2010) 103525, arXiv:1003.5217 [hep-th], 2010. 50+

  • “On Instanton Effects in F-theory” by Ralph Blumenhagen, Andres Collinucci and Benjamin Jurke, JHEP 1008 (2010) 079, arXiv:1002.1894 [hep-th], 2010. 50+

  • “Global F-theory GUTs” by Ralph Blumenhagen, Thomas W. Grimm, Benjamin Jurke and Timo Weigand, Nucl.Phys. B829 (2010) 325-369, arXiv:0908.1784 [hep-th], 2009. 100+

  • “F-theory uplifts and GUTs” by Ralph Blumenhagen, Thomas W. Grimm, Benjamin Jurke and Timo Weigand, JHEP 0909 (2009) 053, arXiv:0906.0013 [hep-th], 2009. 50+

Presentations

Mathematical Physics

Technical / Expert Talks

  • 07/2012: “Scanning for Swiss Cheese Geometries“, PDF slides, presented at the String Math 2012 conference in Bonn, Germany.
  • 06/2012: “Scanning for Swiss Cheese Geometries“, PDF slides, presented at the String Phenomenology 2012 conference in Cambridge, UK.
  • 01/2012: “The Geometry of the LARGE Volume Scenario“, PDF slides, presented at the theory seminar of the MPI of Physics in Munich, Germany.
  • 09/2011: “Line bundle valued Cohomology on Toric Varieties“, PDF slides, presented at the AMS Eastern Sectional Meeting #1072 at Cornell University, Ithaca, USA.
  • 06/2011: “Computational Tools for String Phenomenology“, PDF slides, presented at the Theory seminar at Northeastern University, Boston, USA.
  • 06/2011: “Cohomology of Toric Varieties and Applications“, PDF slides, presented at the String Math 2011 conference in Philadelphia, USA.
  • 07/2010: “Aspects in F-theory model building“, PDF slides, presented at the IMPRS/GK Young Scientists Workshop 2010 at Castle Ringberg, Germany.
  • 07/2010: “A Computational Tool for Line Bundle Cohomologies“, PDF slides, presented at the String Phenomenology 2010 conference in Paris, France.
  • 07/2009: “F-Theory GUTs“, PDF slides, presented at the IMPRS/GK Young Scientists Workshop 2009 at Castle Ringberg, Germany.
  • 01/2009: “String theory: A general overview & current ‘hot’ topics“, PDF slides, presented at the Graduiertenseminar at Universität Würzburg, Germany.
  • 10/2007: “Special Holonomy in Gauge Theory“, PDF slides, presented during the 6th IMPRS workshop as part of my PhD application at the MPI, Munich, Germany.

Public Scientific Talks

  • 08/2012: “Explain like I’m 5: The Higgs Boson“, PDF slides, presented at the Boston Security Meetup at the JobSpring office in Boston, USA.
  • 10/2011: “Quantum Computers & Cryptography“, PDF slides, presented at the Boston Security Meetup at the JobSpring office in Boston, USA.
  • 04/2011: “Teilchenphysik und der LHC“, presented for a school class at the MPI, Munich, Germany.

Downloads

Lecture Notes

During my time of undergraduate study I did typeset a number of lecture notes in \(\LaTeX\) for exam preparations. The resulting PDFs are still circling around at the the physics and mathematics department of the University of Bielefeld.

Physics

  • WS ’03/’04 – SS ’04: Kögerler, “Klassische Mechanik, Spezielle Relativitätstheorie, Quantenmechanik“, PDF (in German)
  • WS ’04/’05: Reimann, “Statistische Mechanik“, PDF (in German)
  • SS ’05: Laine, “Symmetrien in der Physik“, PDF (in German)

Mathematics

  • WS ’02/’03: Frøyshov: “Differentialgeometrie“, PDF (in German)
  • SS ’04 – SS ’05: Frøyshov: “Komplexe Analysis und Geometrie“, PDF (in German)

Note: The documents contain a number of errors that have not been corrected. Nevertheless, as some of those notes are still kind of “in demand” and are in wide circulation, I will offer them for download regardless of any errors—just be careful and do not blindly trust the text.

Theses

  • 12/2010: “Nonperturbative Type IIB Model Building in the F-theory Framework“, PDF — also available as a book, dissertation in mathematical physics, supervised by R. Blumenhagen at the MPP/LMU Munich.
  • 04/2008: “Dimensional Reduction of Spin(7)-Instantons“, PDF, mathematics diploma thesis, supervised by K. Frøyshov at the University of Bielefeld.
  • 07/2007: “Semi-Realistic Orbifold Compactification of Heterotic Strings“, PDF, physics diploma thesis, supervised by R. Kögerler at the University of Bielefeld.