We review free fermion, melting crystal, and matrix model representations of wall-crossing phenomena on local, toric Calabi-Yau manifolds. We consider 
                  both unrefined and refined BPS counting of  closed BPS states involving D2- and D0-branes  bound to a D6-brane, as well as open BPS states involving open D2-branes ending on an additional 
                  D4-brane. Appropriate limit of these constructions provides, among the others, matrix  model representation of refined and unrefined topological string amplitudes.

Piotr Su&#x142;kowski

BPS States, Crystals, and Matrices

We briefly review an algorithmic strategy to explore the landscape of heterotic <svg style="vertical-align:-3.25793pt;width:51.575001px;" id="M2" height="14.3875" version="1.1" viewBox="0 0 51.575001 14.3875" width="51.575001"  xmlns="http://www.w3.org/2000/svg">
	<g transform="matrix(1.25,0,0,-1.25,0,14.3875)">
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			<text transform="matrix(1,0,0,-1,-71.95,63.79)">
				<tspan style="font-size: 12.50px; " x="0" y="0">𝐸</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-63.02,60.66)">
				<tspan style="font-size: 8.75px; " x="0" y="0">8</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-55.37,63.79)">
				<tspan style="font-size: 12.50px; " x="0" y="0">×</tspan>
				<tspan style="font-size: 12.50px; " x="10.777586" y="0">𝐸</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-35.66,60.66)">
				<tspan style="font-size: 8.75px; " x="0" y="0">8</tspan>
			</text>

		</g>
	</g>
</svg> vacua, in the context of compactifying smooth Calabi-Yau threefolds with vector bundles. The Calabi-Yau threefolds are algebraically realised as hypersurfaces in toric varieties, and a large class of vector bundles are constructed thereon as monads. In the spirit of searching for standard-like heterotic
vacua, emphasis is placed on the integer combinatorics of the model-building programme.

Seung-Joo Lee

Combinatorics in <svg style="vertical-align:-0.20474pt" height="12.0625" version="1.1" viewBox="0 0 44.200001 12.0625" width="44.200001" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.738)"><path id="x1D4A9" d="M569 131h1q35 55 122 263q82 196 138 256q34 37 74 37q23 0 37.5 -12.5t14.5 -33.5t-12.5 -33.5t-30.5 -12.5q-17 0 -32 12.5t-15 32.5h-3q-48 -25 -151 -277q-33 -82 -62 -146q-29 -63 -68 -125q-45 -71 -86 -105h-20q26 106 32 310q5 189 27 265l-1 1&#xA;q-61 -82 -143 -248q-93 -184 -150 -256q-59 -74 -123 -74q-34 0 -57 22.5t-23 54.5q0 29 17 47.5t42 18.5q21 0 36.5 -15t15.5 -36q0 -18 -12 -31.5t-30 -13.5q-9 0 -16 4h-3q1 -9 10 -15.5t21 -6.5q51 0 105.5 70.5t132.5 227.5q157 318 252 357l13 -11q-14 -50 -26 -267&#xA;q-8 -166 -27 -260z" /></g><g transform="matrix(.017,-0,0,-.017,21.26,11.738)"><path id="x3D" d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" /></g><g transform="matrix(.017,-0,0,-.017,35.964,11.738)"><path id="x31" d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" /></g></svg> Heterotic Vacua

I generalize the deconstruction lattice formulation of Endres and Kaplan to two-dimensional super-QCD with eight supercharges, denoted by (4,4), and bifundamental matter. I specialize to a particularly interesting (4,4) gauge theory, with gauge group <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>U</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo><mml:mo>×</mml:mo><mml:mi>U</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mi>f</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:math>, and 
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>U</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mi>f</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:math> being weakly gauged. It describes the infrared limit of the D1/D5 brane system, which has been studied extensively as an example of the AdS<sub>3</sub>/CFT<sub>2</sub> correspondence. The construction here preserves two supercharges exactly and has a lattice structure quite similar to that which has previously appeared in the deconstruction approach, that is, site, link, and diagonal fields with both the Bose and Fermi statistics. I remark on possible applications of the lattice theory that would test the AdS<sub>3</sub>/CFT<sub>2</sub> correspondence, particularly one that would exploit the recent worldsheet instanton analysis of Chen and Tong.

Joel Giedt

A Deconstruction Lattice Description of the D1/D5 Brane World-Volume Gauge Theory

Novel nonstandard techniques for the computation of
cohomology classes on toric varieties are summarized. After an introduction of the basic definitions and properties of toric geometry, we discuss a
specific computational algorithm for the determination of the dimension of
line-bundle-valued cohomology groups on toric varieties. Applications to the computation of chiral massless matter spectra in string compactifications are discussed, and using the software package <i  >cohomCalg</i>, its utility
is highlighted on a new target space dual pair of <svg style="vertical-align:-2.21957pt;width:33.794998px;" id="M1" height="14.57625" version="1.1" viewBox="0 0 33.794998 14.57625" width="33.794998"  xmlns="http://www.w3.org/2000/svg">
	<g transform="matrix(1.25,0,0,-1.25,0,14.57625)">
		<text transform="matrix(1,0,0,-1,0.498,2.711)">
			<tspan style="font-size: 12.50px; " x="0" y="0">(</tspan>
			<tspan style="font-size: 12.50px; " x="4.1635389" y="0">0</tspan>
			<tspan style="font-size: 12.50px; " x="10.415099" y="0">,</tspan>
			<tspan style="font-size: 12.50px; " x="15.616397" y="0">2</tspan>
			<tspan style="font-size: 12.50px; " x="21.867956" y="0">)</tspan>
		</text>

	</g>
</svg> heterotic string models.

Ralph Blumenhagen

Benjamin Jurke

Thorsten Rahn

Computational Tools for Cohomology of Toric Varieties

Theories of dark matter that support bound states are an intriguing possibility for the identity of the missing mass of the Universe. This article proposes a class of models of supersymmetric composite dark matter where the interactions with the Standard Model communicate supersymmetry breaking to the dark sector. In these models, supersymmetry breaking can be treated as a perturbation on the spectrum of bound states. Using a general formalism, the spectrum with leading supersymmetry effects is computed without specifying the details of the binding dynamics. The interactions of the composite states with the Standard Model are computed, and several benchmark models are described. General features of nonrelativistic supersymmetric bound states are emphasized.

Siavosh R. Behbahani

Martin Jankowiak

Tomas Rube

Jay G. Wacker

Nearly Supersymmetric Dark Atoms

This is a short review of recent constructions of new Calabi-Yau threefolds with small Hodge numbers and/or nontrivial fundamental group, which are of particular interest for model building in the context of heterotic string theory. The two main tools are topological transitions and taking quotients by actions of discrete groups. Both of these techniques can produce new manifolds from existing ones, and they have been used to bring many new specimens to the previously sparse corner of the Calabi-Yau zoo, where both Hodge numbers are small. Two new manifolds are also obtained here from hyperconifold transitions, including the first example with fundamental group <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math>, the smallest non-Abelian group.

Rhys Davies

The Expanding Zoo of Calabi-Yau Threefolds

We present the complete classification of smooth toric Fano threefolds, known
to the algebraic geometry literature, and perform some preliminary analyses
in the context of brane tilings and Chern-Simons theory on M2-branes probing
Calabi-Yau fourfold singularities. We emphasise that these 18 spaces should be
as intensely studied as their well-known counterparts: the del Pezzo surfaces.

Amihay Hanany

Yang-Hui He

Chern-Simons: Fano and Calabi-Yau

The examination of roots of constrained polynomials dates back at least to
Waring and to Littlewood. However, such delicate structures as fractals and
holes have only recently been found. We study the space of roots to certain
integer polynomials arising naturally in the context of Calabi-Yau spaces, notably
Poincar&#233; and Newton polynomials, and observe various salient features
and geometrical patterns.

Polynomial Roots and Calabi-Yau Geometries

We discuss recent constructions of global F-theory GUT models and explain how to make use of toric geometry to do calculations within this framework. After introducing the basic properties of global F-theory GUTs, we give a self-contained review of toric geometry and introduce all the tools that are necessary to construct and analyze global F-theory models. We will explain how to systematically obtain a large class of compact Calabi-Yau fourfolds which can support F-theory GUTs by using the software package PALP.

Johanna Knapp

Maximilian Kreuzer

Toric Methods in F-Theory Model Building

We study the decay of a <svg style="vertical-align:-0.0pt;width:16.7875px;" id="M2" height="16.049999" version="1.1" viewBox="0 0 16.7875 16.049999" width="16.7875"  xmlns="http://www.w3.org/2000/svg">
	<g transform="matrix(1.25,0,0,-1.25,0,16.05)">
		<g transform="translate(72,-59.16)">
			<text transform="matrix(1,0,0,-1,-71.95,59.21)">
				<tspan style="font-size: 12.50px; " x="0" y="0">𝑍</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-61.42,67.71)">
				<tspan style="font-size: 6.25px; " x="0" y="0">′</tspan>
			</text>

		</g>
	</g>
</svg>-boson into <svg style="vertical-align:-0.16302pt;width:12.8625px;" id="M3" height="10.5375" version="1.1" viewBox="0 0 12.8625 10.5375" width="12.8625"  xmlns="http://www.w3.org/2000/svg">
	<g transform="matrix(1.25,0,0,-1.25,0,10.5375)">
		<g transform="translate(72,-63.57)">
			<text transform="matrix(1,0,0,-1,-71.95,63.79)">
				<tspan style="font-size: 12.50px; " x="0" y="0">𝑈</tspan>
			</text>

		</g>
	</g>
</svg>-unparticle and a photon. The extended Landau-Yang theorem is used. The clear photon signal would make the decay <svg style="vertical-align:-2.34499pt;width:65.824997px;" id="M4" height="18.975" version="1.1" viewBox="0 0 65.824997 18.975" width="65.824997"  xmlns="http://www.w3.org/2000/svg">
	<g transform="matrix(1.25,0,0,-1.25,0,18.975)">
		<g transform="translate(72,-56.82)">
			<text transform="matrix(1,0,0,-1,-71.95,59.21)">
				<tspan style="font-size: 12.50px; " x="0" y="0">𝑍</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-61.42,67.71)">
				<tspan style="font-size: 6.25px; " x="0" y="0">′</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-53.06,59.21)">
				<tspan style="font-size: 12.50px; " x="0" y="0">→</tspan>
				<tspan style="font-size: 12.50px; " x="17.12911" y="0">𝛾</tspan>
				<tspan style="font-size: 12.50px; " x="23.480635" y="0">𝑈</tspan>
			</text>

		</g>
	</g>
</svg> as an additional contribution mode for study of unparticle physics.

G. A. Kozlov

I. N. Gorbunov

On Decays of <svg style="vertical-align:-0.0pt" height="17.7125" version="1.1" viewBox="0 0 16.5375 17.7125" width="16.5375" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,17.65)"><path id="x1D44D" d="M698 636l-541 -596q60 -5 176 -5q91 0 138.5 5t69.5 24q44 36 85 124l29 -15q-38 -125 -64 -173h-559l-9 16l545 598h-182q-81 0 -109 -8t-48 -31q-26 -29 -55 -103l-29 3q23 86 42 200h22q11 -16 21 -20.5t34 -4.5h428z" /></g><g transform="matrix(.012,-0,0,-.012,12.313,9.488)"><path id="x2032" d="M227 744l-123 -338l-31 15l73 368q12 3 41.5 -8t36.5 -20z" /></g></svg> into Unparticle Stuff

Global symmetries play an important role in classifying the spectrum of a gauge theory. 
In the context of the <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.17555pt;width:71.0625px;" id="M2" height="15" version="1.1" viewBox="0 0 71.0625 15" width="71.0625">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><use xlink:href="#x1D434"></use></g><g transform="matrix(.017,-0,0,-.017,12.523,12.162)"><use xlink:href="#x1D451"></use></g><g transform="matrix(.017,-0,0,-.017,21.957,12.162)"><use xlink:href="#x1D446"></use></g><g transform="matrix(.017,-0,0,-.017,30.116,12.162)"><use xlink:href="#x2F"></use></g><g transform="matrix(.017,-0,0,-.017,37.12,12.162)"><use xlink:href="#x1D436"></use></g><g transform="matrix(.017,-0,0,-.017,49.104,12.162)"><use xlink:href="#x1D439"></use></g><g transform="matrix(.017,-0,0,-.017,59.677,12.162)"><use xlink:href="#x1D447"></use></g>

		
	
</svg> duality, global baryon-like symmetries are specially interesting. In the gravity side, they correspond to vector fields in <i>AdS</i> arising from KK reduction of the SUGRA <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-2.29482pt;width:10.2px;" id="M3" height="13.3" version="1.1" viewBox="0 0 10.2 13.3" width="10.2">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,8.863)"><path id="x1D45D" d="M570 304q0 -108 -87 -199q-40 -42 -94.5 -74t-105.5 -43q-41 0 -65 11l-29 -141q-9 -45 -1.5 -58t45.5 -16l26 -2l-5 -29l-241 -10l4 26q51 10 67.5 24t26.5 60l113 520q-54 -20 -89 -41l-7 26q38 28 105 53l11 49q20 25 77 58l8 -7l-17 -77q39 14 102 14q82 0 119 -36&#xA;t37 -108zM482 289q0 114 -113 114q-26 0 -66 -7l-70 -327q12 -14 32 -25t39 -11q59 0 118.5 81.5t59.5 174.5z"></path></g>

		
	
</svg>-form potentials. We concentrate on the <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-3.25793pt;width:83.724998px;" id="M4" height="16.450001" version="1.1" viewBox="0 0 83.724998 16.450001" width="83.724998">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><use xlink:href="#x1D434"></use></g><g transform="matrix(.017,-0,0,-.017,12.523,12.162)"><use xlink:href="#x1D451"></use></g><g transform="matrix(.017,-0,0,-.017,21.957,12.162)"><use xlink:href="#x1D446"></use></g>

			<g transform="matrix(.012,-0,0,-.012,30.113,16.25)"><path id="x34" d="M456 178h-96v-72q0 -51 12.5 -62.5t72.5 -16.5v-27h-256v27q65 5 78 17t13 62v72h-260v28q182 271 300 426h40v-407h96v-47zM280 225v295h-2q-107 -148 -196 -295h198z"></path></g>

			<g transform="matrix(.017,-0,0,-.017,36.45,12.162)"><use xlink:href="#x2F"></use></g><g transform="matrix(.017,-0,0,-.017,43.453,12.162)"><use xlink:href="#x1D436"></use></g><g transform="matrix(.017,-0,0,-.017,55.438,12.162)"><use xlink:href="#x1D439"></use></g><g transform="matrix(.017,-0,0,-.017,66.011,12.162)"><use xlink:href="#x1D447"></use></g>

			<g transform="matrix(.012,-0,0,-.012,77.337,16.25)"><path id="x33" d="M285 378v-2q65 -13 102 -54.5t37 -97.5q0 -57 -30.5 -104.5t-74 -75t-85.5 -42t-72 -14.5q-31 0 -59.5 11t-40.5 23q-19 18 -16 36q1 16 23 33q13 10 24 0q58 -51 124 -51q55 0 88 40t33 112q0 64 -39 96.5t-88 32.5q-29 0 -64 -11l-6 29q77 25 118 57.5t41 84.5&#xA;q0 45 -26.5 69.5t-68.5 24.5q-67 0 -120 -79l-20 20l43 63q51 56 127 56h1q66 0 107 -37t41 -95q0 -42 -31 -71q-22 -23 -68 -54z"></path></g>

		
	
</svg> case, which presents very interesting characteristic features. Following arXiv:1004.2045, we review
aspects of such symmetries, clarifying along the way some arguments in that reference. As a byproduct, and in a slightly unrelated context, we also study <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.1881pt;width:15.9625px;" id="M5" height="12.0625" version="1.1" viewBox="0 0 15.9625 12.0625" width="15.9625">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,11.738)"><path id="x1D4B5" d="M407 519l18 -8q-26 -50 -58 -74t-80 -24q-50 0 -90 32q-38 32 -38 83q0 60 52 109q53 50 145 50q52 0 108 -13q67 -16 94 -26l92 -36q71 46 150 46q55 0 83.5 -16.5t28.5 -43.5q0 -24 -33 -41t-83 -17q-53 0 -133 26q-57 -66 -116 -236q3 -1 11 -1q60 1 93 27l14 -17&#xA;q-56 -59 -118 -59q-15 0 -18 1q-54 -143 -158 -221q107 -36 157 -36q79 0 132 36.5t72 102.5l20 -1q-14 -85 -71.5 -131t-150.5 -46q-34 0 -76 11q-50 13 -121 38q-74 -43 -162 -43q-112 0 -112 60q0 24 33 41t83 17q46 0 142 -31q58 55 120 215q-3 1 -12 1q-52 0 -95 -32&#xA;l-17 16q60 65 126 65q13 0 17 -1q67 163 157 241q-43 17 -88 32q-31 11 -85 21q-56 12 -105 12q-64 0 -100 -40q-35 -40 -35 -80q0 -39 25 -62t62 -23q42 0 68.5 17t51.5 59zM871 598q0 30 -71 30q-62 0 -106 -33q66 -25 112 -25q27 0 46 8.5t19 19.5zM283 51&#xA;q-75 28 -118 28q-27 0 -46 -8.5t-19 -19.5q0 -30 71 -30q65 0 112 30z"></path></g>

		
	
</svg> minimization, focusing on the HVZ theory.

Diego Rodriguez-Gomez

Baryonic Symmetries in <svg style="vertical-align:-3.25793pt" height="16.475" version="1.1" viewBox="0 0 84.199997 16.475" width="84.199997" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path id="x1D434" d="M716 28l-8 -28h-254l8 28q55 5 66 17.5t5 47.5l-30 145h-232l-74 -138q-21 -43 -11 -54.5t72 -17.5l-6 -28h-235l8 28q53 7 73.5 21t53.5 70l319 540l33 8q6 -43 33 -176l80 -381q10 -49 26.5 -63t72.5 -19zM495 281l-49 264h-2l-149 -264h200z" /></g><g transform="matrix(.017,-0,0,-.017,12.523,12.162)"><path id="x1D451" d="M530 686q-79 -330 -126 -595q-5 -24 4 -24q22 0 77 53l16 -24q-42 -49 -88 -78.5t-72 -29.5q-37 0 -19 83l21 99h-2q-62 -83 -153 -141q-65 -41 -97 -41q-28 0 -48 31.5t-20 91.5q0 71 32.5 144t88.5 118q36 30 94 52.5t94 22.5q38 0 68 -13l29 158q7 40 2 47.5t-38 7.5&#xA;h-35l1 26q39 4 76 13.5t58.5 17t27.5 7.5q16 0 9 -26zM387 375q-11 11 -38.5 20t-51.5 9q-45 0 -79 -23q-46 -32 -77.5 -107.5t-31.5 -143.5q0 -40 9.5 -58.5t23.5 -18.5q40 0 113.5 70t99.5 118z" /></g><g transform="matrix(.017,-0,0,-.017,21.957,12.162)"><path id="x1D446" d="M457 488l-30 -3q-17 148 -131 148q-53 0 -84.5 -34.5t-31.5 -82.5q0 -42 25.5 -72t74.5 -62l33 -22q63 -42 95 -85t32 -102q0 -84 -67 -137t-163 -53q-58 0 -113 22t-70 43l-4 152l27 4q4 -32 15 -62.5t31 -59.5t53.5 -47t76.5 -18q56 0 92 35t36 96q0 39 -25 70t-78 68&#xA;l-31 22q-32 23 -53.5 41.5t-45 57t-23.5 77.5q0 82 58 132.5t156 50.5q46 0 101 -17l18.5 -6t17 -6t8.5 -3q-4 -55 0 -147z" /></g><g transform="matrix(.012,-0,0,-.012,30.113,16.25)"><path id="x1D7D2" d="M476 255v-111h-64v-144h-145v144h-248v113l313 431h80v-433h64zM60 255h208v294z" /></g><g transform="matrix(.017,-0,0,-.017,36.688,12.162)"><path id="x2F" d="M368 703l-264 -866h-60l265 866h59z" /></g><g transform="matrix(.017,-0,0,-.017,43.691,12.162)"><path id="x1D436" d="M682 629q-1 -16 -1.5 -72t-2.5 -86l-31 -4q-5 92 -51 129t-139 37q-100 0 -177 -49t-116 -125t-39 -162q0 -122 66 -201t182 -79q83 0 137 42.5t112 128.5l26 -15q-12 -31 -42.5 -88t-45.5 -75q-139 -27 -199 -27q-148 0 -243 81.5t-95 226.5q0 173 129.5 274.5&#xA;t325.5 101.5q114 0 204 -38z" /></g><g transform="matrix(.017,-0,0,-.017,55.675,12.162)"><path id="x1D439" d="M599 650l-18 -160l-30 -2q-2 70 -11 94q-5 16 -26 24t-75 8h-94q-27 0 -33.5 -6.5t-12.5 -32.5l-43 -226h108q52 0 72.5 5t31 18t28.5 52h28l-40 -200h-28q-1 42 -6 56.5t-24.5 21t-70.5 6.5h-108l-32 -177q-13 -65 1 -80.5t88 -22.5l-8 -28h-279l6 28q61 5 77.5 20.5&#xA;t29.5 81.5l72 387l7.5 40.5t1 26.5t-4 18t-15.5 10t-24 6t-37 4l8 28h461z" /></g><g transform="matrix(.017,-0,0,-.017,66.248,12.162)"><path id="x1D447" d="M649 676l-22 -187l-33 -2q3 56 -12 94q-8 20 -31.5 26.5t-86.5 6.5h-74l-90 -491q-4 -23 -6 -36.5t1 -25t7 -16.5t18 -9t27 -5t41 -3l-6 -28h-286l4 28q68 5 84 18.5t28 76.5l94 491h-55q-74 0 -100.5 -6t-41.5 -23q-24 -29 -54 -98l-32 1q32 98 53 188h22q7 -18 15 -22&#xA;t37 -4h417q23 0 33.5 5t25.5 21h23z" /></g><g transform="matrix(.012,-0,0,-.012,77.575,16.25)"><path id="x1D7D1" d="M58 524l-21 12q80 152 229 152q73 0 119 -41q45 -41 45 -96q0 -40 -21.5 -74.5t-62.5 -52.5q57 -20 89.5 -68.5t32.5 -109.5q0 -110 -86 -185t-214 -75q-69 0 -110.5 24.5t-41.5 65.5q0 26 18.5 43t46.5 17q45 0 96 -57q39 -43 79 -43q45 0 71.5 34t26.5 88q0 75 -49 121&#xA;q-25 23 -56 39q-34 17 -97 38v17q69 21 100 53t31 78q0 103 -99 103q-40 0 -69.5 -19t-56.5 -64z" /></g></svg>: An Overview

I give an elementary introduction to the key algorithm used in recent applications
of computational algebraic geometry to the subject of string phenomenology. I
begin with a simple description of the algorithm itself and then give 3 examples of its use in
physics. I describe how it can be used to obtain constraints on flux parameters, how it can
simplify the equations describing vacua in 4D string models, and lastly how it can be used to
compute the vacuum space of the electroweak sector of the MSSM.

James Gray

A Simple Introduction to Gr&#246;bner Basis Methods in String Phenomenology

An analytic construction of compact Calabi-Yau manifolds with del Pezzo singularities
is found. We present complete intersection CY manifolds for all del Pezzo singularities
and study the complex deformations of these singularities. An example of the quintic CY
manifold with del Pezzo 6 singularity and some number of conifold singularities is studied
in detail. The possibilities for the &#x2018;&#x2018;geometric&#x2019;&#x2019; and ISS mechanisms of dynamical SUSY
breaking are discussed. As an example, we construct the ISS vacuum for the del Pezzo 6
singularity.

Dmitry Malyshev

Del Pezzo Singularities and SUSY Breaking

About this journal

<p><em>Advances in High Energy Physics</em> publishes the results of theoretical and experimental research on the nature of, and interaction between, energy and matter.</p>


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<p>Chief Editor, Professor Seidel, is a professor in the Department of Physics and Astronomy at the University of New Mexico. She is a collaborator on the ATLAS experiment at the Large Hadron Collider, researching high-energy collider physics.</p>


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Advances in High Energy Physics - Table of contents 2011

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Advances in High Energy Physics publishes the results of theoretical and experimental research on the nature of, and interaction between, energy and matter.

Advances in High Energy Physics