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<!DOCTYPE html>
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Plain-Academic by Vasilios Mavroudis
Released under the Simplified BSD License/FreeBSD (2-clause) License.
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<title>Bernhard Böhmler's website</title>
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<li><a href="index.html#publications">Publications</a></li>
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<div style="font-family: 'Oswald', sans-serif; font-size: 32px;"><b>Bernhard Böhmler</b></div><br>
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<img class="img-responsive" src="bernhard222.jpg" alt=""></div>
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<p><b>Office:</b> C 411 (main building) <br> Leibniz University Hannover <br> Faculty of Mathematics and Physics <br> Institute of Algebra, Number Theory <br> and Discrete Mathematics
<br> Welfengarten 1 <br> 30167 Hannover <br> Germany
<br>
</p>
<p><b>Phone:</b></p>
<p>+49 (0)511 762 32 09 </p>
<p><b>E-Mail:</b></p>
<p><i> boehmler [at] math [dot] uni-hannover [dot] de </i></p>
<p><b>Office hours:</b></p>
<p>by appointment via e-mail </p>
<br>
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<h2 id="about">About me</h2>
<div style="margin-top:3%; text-align:justify;">
<p>Hello! </p>
<p> My name is Bernhard Böhmler and I am a postdoctoral researcher in the working group of <a href="https://www.iazd.uni-hannover.de/de/cuntz">Michael Cuntz</a> at the Leibniz University Hannover. </p>
<p> Before that, I was a doctoral student at the RPTU Kaiserslautern-Landau under the supervision of <a href="https://math.rptu.de/ags/agag/personen/leitung/lassueur/seite"> Caroline Lassueur</a>.</p>
<p> The main focus of my dissertation - which is located in the area of modular representation theory of finite groups - lies on <strong>trivial source modules</strong>. They are also known as $p$-permutation modules and arise naturally
in this context. They are the building blocks for p-permutation equivalences, Puig equivalences and splendid derived equivalences. </p>
<p> In order to do calculations with trivial source modules the ordinary characters of their lifts from positive characteristic $p$ to characteristic $0$ are of particular interest. The “trivial source character tables” or “species tables
of the trivial source ring” collect information about the character values of trivial source $kG$ - modules with all possible vertices, as well as those of their Brauer constructions.
</p>
<p>
In my doctoral thesis, I examine trivial source modules and their character tables both theoretically and using computer algebra. My <a href="poster.pdf">poster</a> gives a small overview of trivial source character tables and
an example. My doctoral thesis can be found <a href="https://doi.org/10.26204/KLUEDO/8356">here</a>.
</p>
<p> I gratefully acknowledge financial support by DFG SFB-TRR 195: ‘Symbolic Tools in Mathematics and their Application’ and by the German Academic Exchange Service (DAAD). </p>
<p> Outside of my research I am an enthusiastic amateur musician and I like to play chess. </p>
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<h2 id="research_interests">Research interests</h2>
<ul>
<li>Group theory </li>
<li>Modular and ordinary representation theory of finite groups </li>
<li>Representation theory of finite-dimensional algebras </li>
<li>Auslander-Reiten theory </li>
<li>Homological algebra </li>
<li>Frieze patterns </li>
</ul>
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<!-- Publications -->
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<h2 id="publications">Publications</h2>
<strong>In Progress</strong><br/>
<ul>
<li class="paper" words="add, your, keywords, here"> <a> An algorithm to compute trivial source character tables of finite groups
</a></li>
<li class="paper" words="add, your, keywords, here"> <a> Trivial source characters in blocks of domestic representation type
</a></li>
</ul>
<strong>Submitted</strong><br/>
<ul>
<li class="paper" words="add, your, keywords, here"> <a href="SL2_ZNZ.pdf">Frieze patterns over finite commutative local rings </a> (with Michael Cuntz) </li>
<li class="paper" words="add, your, keywords, here"> <a href="FrobeniusGroups.pdf">Trivial source character tables of Frobenius groups of type (C<sub>p</sub> × C<sub>p</sub>) ⋊ H </a> (with Caroline Lassueur) </li>
</ul>
<strong>Published articles in journals</strong><br/>
<ul>
<li class="paper" words="add, your, keywords, here"><a href="https://link.springer.com/article/10.1007/s10468-022-10140-7">On the extension-closed property for the subcategory Tr($\Omega$<sup>2</sup>(mod$-A$))</a> (with René Marczinzik) </li>
<li class="paper" words="add, your, keywords, here"><a href="https://doi.org/10.1016/j.jalgebra.2022.01.024">Trivial source character tables of SL<sub>2</sub>$(q)$</a> (with Caroline Lassueur and Niamh Farrell) </li>
<li class="paper" words="add, your, keywords, here"><a href="https://doi.org/10.1016/j.jalgebra.2021.06.037">A cluster tilting module for a representation-infinite block of a group algebra</a> (with René Marczinzik) </li>
<li class="paper" words="add, your, keywords, here"><a href="https://doi.org/10.1016/j.jalgebra.2018.03.002"> On a conjecture about Morita algebras </a> (with René Marczinzik) </li>
</ul>
<strong>Other</strong><br/>
<ul>
<li class="paper" words="add, your, keywords, here">An appendix to the article <a href="https://doi.org/10.1016/j.jalgebra.2024.03.014">Selfextensions of modules over group algebras</a> (with René Marczinzik) </li>
</ul>
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<h2 id="teaching">Teaching</h2>
<strong> Summer semester 2024 </strong><br/>
<ul>
<li class="paper" words="add, your, keywords, here">B.Sc. lecture: Discrete Mathematics (assistant)</li>
</ul>
<strong> Winter semester 2023/2024 </strong><br/>
<ul>
<li class="paper" words="add, your, keywords, here">B.Sc. lecture: Higher Mathematics 1 for Engineers (tutor)</li>
</ul>
<strong> Summer semester 2022 </strong><br/>
<ul>
<li class="paper" words="add, your, keywords, here">B.Sc. lecture: Character Theory of Finite Groups (assistant) </li>
<li class="paper" words="add, your, keywords, here">B.Sc. lecture: Higher Mathematics 4 for Engineers (assistant) </li>
</ul>
<strong> Winter semester 2021/2022 </strong><br/>
<ul>
<li class="paper" words="add, your, keywords, here">No teaching due to a research stay at the University of California, Santa Cruz</li>
</ul>
<strong> Summer semester 2021 </strong><br/>
<ul>
<li class="paper" words="add, your, keywords, here">M.Sc. lecture: Cohomology of Groups (assistant) </li>
<li class="paper" words="add, your, keywords, here">B.Sc. lecture: Higher Mathematics 4 for Engineers (assistant) </li>
</ul>
<strong> Winter semester 2020/2021 </strong><br/>
<ul>
<li class="paper" words="add, your, keywords, here">M.Sc. lecture: Representation Theory of Finite Groups (assistant) </li>
</ul>
<strong> Summer semester 2019 </strong><br/>
<ul>
<li class="paper" words="add, your, keywords, here">B.Sc. lecture: Character Theory of Finite Groups (assistant) </li>
</ul>
<strong> Winter semester 2016/2017 </strong><br/>
<ul>
<li class="paper" words="add, your, keywords, here">B.Sc. lecture: Higher Mathematics 3 for Engineers (tutor) </li>
</ul>
<strong> Winter semester 2015/2016 </strong><br/>
<ul>
<li class="paper" words="add, your, keywords, here">B.Sc. lecture: Higher Mathematics 3 for Electrical Engineering Technicians (tutor) </li>
</ul>
<strong> Winter semester 2014/2015 </strong><br/>
<ul>
<li class="paper" words="add, your, keywords, here">B.Sc. lecture: Higher Mathematics 3 for Engineers (tutor) </li>
</ul>
<strong> Summer semester 2014 </strong><br/>
<ul>
<li class="paper" words="add, your, keywords, here">B.Sc. lecture: Higher Mathematics 2 for Engineers (tutor) </li>
</ul>
<strong> Winter semester 2013/2014 </strong><br/>
<ul>
<li class="paper" words="add, your, keywords, here">B.Sc. lecture: Higher Mathematics 3 for Engineers (tutor) </li>
</ul>
<strong> Summer semester 2013 </strong><br/>
<ul>
<li class="paper" words="add, your, keywords, here">B.Sc. lecture: Algebra for Mathematicians (tutor) </li>
</ul>
<strong> Winter semester 2012/2013 </strong><br/>
<ul>
<li class="paper" words="add, your, keywords, here">B.Sc. lecture: Higher Mathematics 1 for Engineers (tutor) </li>
</ul>
<strong> Summer semester 2012 </strong><br/>
<ul>
<li class="paper" words="add, your, keywords, here">B.Sc. lecture: Geometry for Mathematicians (tutor) </li>
</ul>
<strong> Winter semester 2011/2012 </strong><br/>
<ul>
<li class="paper" words="add, your, keywords, here">B.Sc. lecture: Higher Mathematics 1 for Engineers (tutor) </li>
</ul>
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