**Research/Areas of Interest:**

Physics of elementary particles

The Standard Model, gauge theories; also topology, differential geometry and other branches of modern mathematics to better understand quantum gauge theories, the origin of mass and the structure of space-time, matter and all interactions, including gravity.

I am a member of the ATLAS collaboration at the LHC. Studies of Higgs boson and top quarks. The main objective is to find out whether the new particle discovered in 2012 is a minimal Standard Model Higgs, or some other kind. Studies of top quarks are very interesting on their own. Because of very large mass of the top quark, its lifetime is very short, ~ 5x10^{-25} seconds, much shorter that the characteristic time of the strong interactions. As a consequence, top quark decays before any strong interaction effects may take place. This allows a direct access to the information about the quark spin, which is very difficult, if not impossible, for any other quark. Studies of top quarks are very important for other searches, as top quarks will constitute the most important background for almost any final states due to "new physics" and have to be understood very well. We are using very advanced multidimensional analysis techniques, developed by our group (Ben Whitehouse and I).

Topology and geometry of the Universe

In the Standard Cosmological Model (SCM), the starting point is an interpretation of the observed redshift of spectral lines from distant galaxies as a Doppler shift in the frequency of light waves as they travel through an expanding Universe. Acceptance of this hypothesis led to the ideas of the Big Bang and the LambdaCDM, the Standard Model of cosmology.

Remarkably, there exist another explanation of the cosmological redshift. As shown by Irving Ezra Segal, a mathematician and a mathematical physicist, the same axioms of global isotropy and homogeneity of space and time, and its causality properties, are satisfied not only by the Minkowski spacetime R x R^3, but also by a Universe whose geometry is R X S^3. In Segal's model, the geometry of the spatial part of the Universe is that of a three-dimensional hypersurface of a four-dimensional sphere. Locally, it is indistinguishable from the flat Minkowski spacetime. It is the geometry of the Einstein static Universe, which he abandoned when the interpretation of the increase of redshift with distance was universally accepted as evidence for expanding Universe.

If the universe is R1 x S3 but observations are made in flat Minkowski frame, then such an observer measures the "projections" from R1 x S3 into flat R1 x R3. The redshift in Segal's model arises in a geometric way analogously to distortions which appear when making maps using stereographic projection from S^2, a two-dimensional curved surface of a sphere in three dimensions, onto a flat surface of a map, R^2. Segal's theory makes a verifiable prediction for the redshift as a function of distance. The comparison, although in principle very simple, is non-trivial. For more distant objects, one can only estimate the distance using various proxies, for example the magnitude, if one assumes that the chosen sources have the same absolute luminosity.

Surprisingly, Segal's model cannot be falsified with the currently available data. The magnitude-redshift data for supernovae agree very well with SCM, but it also agrees with Segal's model. There exist another independent observable, the number of observed galaxies as a function of redshift z, N(< z). Assuming that galaxies are uniformly distributed in the Universe, their number is proportional to the volume enclosed in a given fixed angular field of view, and the dependence of this volume on the manifold distance is sensitive to the geometry of the Universe.

Two Tufts undergraduate students, Maxwell Kaye and Nathan Burwig, joined me in this analysis. We examined the data from several Hubble Deep Fields, and found that the number of observed galaxies as a function of redshift is also in very good agreement with Segal's model.

We are continuing with a study of these fundamental questions about the topology and geometry of our Universe.

Interestingly, I have also shown recently that one can explain the observed value of the CMB temperature, following Segal's original idea that the CMB appears unavoidably as a result of light traveling many times around a closed spatial part of the R X S^3 Universe.

Magnetic monopoles

I am also a member of MoEDAL, a small collaboration looking for magnetic monopoles at the LHC.

## Education

- PhD, Institute of Nuclear Physics, Krakow, Poland, 1980
- MS, Jagiellonian University, Krakow, Poland, 1975
- Undergraduate, Jagiellonian University, Krakow, Poland, 1975